Preheat oven to 400 degrees and prepare a 9x13 inch dish with non stick spray or butter.
In a medium bowl (or bowl of stand mixer) combine the warm water, yeast, and sugar and allow to proof (rest) for 10 minutes.
To the proofed yeast mixture add the butter, salt, egg, and 2 cups of flour.
Begin mixing on low with dough hook, adding in additional flour 1/2 cup at a time.
Mixture is ready when dough has pulled away from sides of the bowl, and all of the flour is incorporated
NOTE: If you are mixing by hand, add flour as directed and stir in with a spoon. When you are no longer able to stir, place the dough on your floured counter top and knead the rest of the flour in by hand until well incorporated. (2-3 minutes).
Shape your dough into 12 balls and place into prepared pan.
Allow dough to rest for 5 minutes, before placing in the oven.
For the topping:
Mix together the melted butter, garlic, onion, parmesan, and parsley and brush over your rolls right before they go in the oven.
Bake for 12-15 minutes, just until golden brown.