Combine 2 cups flour, sugar, Fleischmann’s® RapidRise® Instant Yeast and salt in a large mixing bowl.
On the stovetop in a saucepan or in a microwave-safe bowl, heat milk, water, and ¼ cup butter until very warm (120-130°F).
Add the warm liquid mixture into the dry ingredients. Beat 2 minutes at medium speed with an electric mixer, scraping bowl occasionally. (This can also be done by hand using a wooden spoon.)
Add the egg and ½ 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, for a make-ahead option, place the dough in a greased bowl, cover with plastic wrap, and allow it to rise in the refrigerator for between 12 to 24 hours.)
For the Garlic Parmesan Topping:
Before shaping rolls, melt the butter. Then, in a separate bowl, stir together the minced garlic and grated parmesan cheese.
For Shaping & Baking the Rolls:
Once dough has risen, divide dough in half. Roll each half to a 12-inch square, about ¼ inch thick. Cut each piece into (6) 12x2-inch strips. Cut each strip into (3) 4x2-inch rectangles. Brush each rectangle with the 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.