Combine 2 cups flour, sugar, Fleischmann’s® RapidRise® Instant Yeast and salt in a large mixer bowl.
Heat milk, water, and 1/4 cup butter until very warm (120° to 130°F). Stir into flour mixture. Beat 2 minutes at medium speed with an electric mixer, scraping bowl occasionally.
Add the egg and 1/2 cup more of the flour. Beat for 2 minutes at high speed. Stir in enough remaining flour to make a soft dough.
Knead on a lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes. (Or, if desired, place dough in a greased bowl, cover with plastic wrap, and allow it to rise in the refrigerator for 12 to 24 hours.)
Divide dough in into 20 even portions and roll each piece into a smooth ball. Brush each dough ball melted butter and sprinkle with a heaping spoonful of the parmesan and garlic mixture. Arrange in rows ¼ inch apart to allow room to expand. Cover and let rise in a warm place for 30 minutes or until doubled in size.
Once rolls are proofed, preheat the oven to 400°F. Bake the rolls for 18 minutes or until golden brown and hollow sounding when you tap on the bottom of a roll.