Pre-heat your oven to the lowest setting then shut it off once it comes to temperature.
Meanwhile, in a large bowl combine all of the dry ingredients including your yeast.
Whisk your eggs well in a small separate bowl then add them along with the cheese, oil and water to your dry ingredients.
Mix well until a dough begins to form. At this point I put my dough in my KitchenAid mixer with the dough hook attachment on the setting 3 or 4 and let it run for ~8min.
If you do not have a mixer, you will have to knead the dough for ~ 10min by hand.
Form your dough into a rough ball shape and place it in a greased bowl, covered with Saran Wrap. Place this inside your previously warmed oven with the door ajar (or some place warm) to rise for 1 hour.
After an hour your dough should have doubled in size. You can now punch it down and put it on a flat surface to begin forming it into buns.
Break the dough into 6 even pieces for large hamburger buns (or 12 for smaller dinner rolls) and roll each ball using your hands and the surface to make it as smooth as possible. Pinch cracks back together, roll again and do your best to keep them as even looking as possible.
Place the rolled dough balls onto a greased baking sheet about 1-2inches apart. Cover them with Saran Wrap and let them rise another 20min.
Pre-heat your oven to 375*F. Meanwhile, Brush the buns with egg yolk and sprinkle additional shredded cheese onto the tops of each bun.
Bake them in the pre-heated oven for 45-50min for large buns or 25-30min for smaller buns.
When the buns are still warm, use a spatula to gently lift the bottoms from the pan, brush with butter and sprinkle parmesan and Italian herbs OR alternatively brush with garlic butter. (You can skip this step if you'd like to freeze them and eat them at a later date or if you are using them strictly for sandwiches/hambuger buns).
Serve warm or freeze in a plastic ziplock for future meals once fully cooled...enjoy!