In a stand mixer, combine 2 Cups of the flour, yeast, sugar, and salt.
Add the milk, butter, water and egg, and mix using the dough hook, adding the remaining flour a little at a time. A shaggy, thick, sticky dough will form.
Continue kneading, either by hand or by mixer until the dough become smooth and springs back when you press it with a finger.
Let the dough rest on the counter for 15 minutes, covered with a barely damp towel.
Sprinkle flour on your countertop, and roll out dough to a rectangle..
Mix the butter, garlic, salt and pepper together, and spread out over the entire surface of the dough.
Add the cheese evenly over the dough.
Roll up, and cut into 12 rolls (I use dental floss for a clean cut).
Place the rolls in your baking dish, cover and let them rise for about an hour - until puffy.
Preheat the oven to 375, and bake for 20 minutes until browned.
Remove from the oven, and brush with butter.