In a small bowl, add the 2 tbsp warm water, yeast and inulin and use a fork to gently stir everything once. Cover with saran wrap and set aside.
In a large bowl, whisk together all of your dry ingredients including; vital wheat gluten, allulose sweetener, oat fiber, lupin flour, coconut flour, baking powder, xanthan gum, cinnamon and salt.
Next, chop the cold butter into rough small chunks (they don't have to be even) and add them to the bowl.
Use a fork or dough blender to cut the butter into the dry ingredients and make the pieces smaller. (I like to use the end of the fork to poke down on the pieces. This may take a bit. Don't worry about the pieces being perfectly small!)
Once the pieces are about the size of mentos as I like to say, you can then add the cold water and heavy cream, along with the yeast mixture from earlier (which, should now be quite foamy).
Stir everything until the dough starts to come together, then use your hands to form a rough ball. Our goal is not to fully blend the dough, but simply to get it to stick together in a ball shape with chunks of butter still easily visible. Add an extra tablespoon of cold water only if needed.
Next, wrap your large ball of dough in plastic wrap and place it in the fridge to chill for 30min.
After 30min you can un-wrap the ball of dough and place it on a greased and lightly vital wheat gluten-floured surface. (I prefer to use two pieces of greased and floured parchment paper for this). If not using parchment paper on the bottom, at least use one piece on top of your dough. This will prevent the rolling pin from sticking to the dough.
Roll the dough out length-wise to get a long rectangle. Fold one side of the dough inwards, then the other like folding a brochure or letter. Gently push any rough edges in to straighten out the shape of your dough. Then turn it 90*. flour the surface and top of the dough again and repeat the first step of rolling it out into a long rectangle..then again fold it like a letter. Repeat this process 4-5 times in total. Your dough may get tough to roll out. If this happens, simply refrigerate and cover the dough for another 30min - 1 hour to allow the gluten time to relax.
After these initial 4-5 folds, refrigerate your dough for 30min. Then repeat for 2 more folds or just until your butter is almost completely blended and streaky rather than chunky. Again, if your dough is super tough, just roll it out as much as you can, wrap it in plastic wrap and refrigerate, then continue to roll after 30min.
Once you are down with rolling and folding, make sure your dough chills for at least 30min prior to the next step.
Take your dough out, un-wrap it and slice it evenly in half. Re-wrap one half and place it back in the fridge for later.
Roll out this piece of croissant dough again, but this time, width-wise AND length-wise to create a large thicker rectangle.
Make sure your dough gets about as thin as you can get it. It will likely be about 1/4 of an inch thick (basically thin but still easy to pick up without breaking).
Cut any weird un-even edges off your rectangle using a sharp knife or pizza cutter (save the dough!) Then for LARGE croissants, cut the rectangle diagonally from one corner to the other into 2 long triangles. For SMALL croissants cut the original rectangle of dough into 2 smaller rectangles by slicing down the center, then slice those 2 rectangles into 4 triangles.
Use the left-over scraps to form one final large croissant by placing the pieces of dough together and rolling them out to form another rough long triangle. (Or form 2 more croissants if making smaller croissants).
Take the triangles and using a knife or pizza cutter, slice just a bit up the middle of the short FLAT side of the triangle (see photos). Then pinch the corners of this side and gently pull them apart slightly (again, see the photos). This just helps our croissants look prettier after rolling them up. Roll the croissants from the bottom (cut-side) up to the very tip of the triangle, then gently press the tip of the triangle into the dough to help the croissant hold together. Don't worry if it's not completely sticking just yet. Repeat this process for all of your croissant triangles.
Place finished croissants on a parchment-lined baking sheet spaced evenly apart. Remove your second-half of the dough from the fridge and repeat this same process.
Once you have all of your croissants on a parchment-lined baking sheet, whisk together your egg and water until smooth, then lightly brush all of the croissants with the mixture. Cover your croissants with plastic wrap (you can tent your plastic wrap by using small up-side down cups in the center of your tray to prevent the plastic wrap from sticking to the dough at all). Then let the croissants rise for ~1 hour - an hour and 20min in a draft-free space around 75° to 80°F, DO NOT put them somewhere particularly warm. If you let them rise past this time, the butter may melt. Also note these croissants will not double in size but rather grow just slightly (about 1.25 to 1.5x in size).
During the last 20min of rising, pre-heat your oven to 375*F. Place your oven rack on a the highest setting if your oven tends to brown more from the bottom-up, place the rack on a lower or middle shelf if it browns more from the top-down.
Very gently brush the croissants with a touch more of the egg mixture IF they seem dry (note - this will cause MORE browning so be careful not to put too much).
Bake the croissants for ~20min or until a golden brown colour. Keep an eye on them. If you find the tops browning too quickly, cover them with tin foil part-way though and keep baking them at a slightly lower temperature to fully cook the centers. (Note - even if the centers come out soft, they do set-up a bit the day after).
Place the finished croissants on a plate to cool slightly, then serve warm with butter and jam or whichever toppings you prefer. Enjoy the Best Keto Croissants!