Combine ¾ cup flour, 2 Tbsp sugar, 1 packet Fleischmann’s RapidRise Yeast, and ½ tsp salt in a large mixer bowl and stir until blended.
Combine ½ cup milk, ¼ cup water, and 2 Tbsp butter in a microwave-safe bowl or measuring cup. Microwave on HIGH in 15 second increments until very warm, but not hot to touch (120 to 130 degrees Fahrenheit when checked with a digital thermometer). The butter won’t melt completely. Add milk mixture to flour mixture.
Add ¼ cup flour; beat 2 minutes at high speed. Stir in just enough remaining flour (1¾ to 2 cups more) so that the dough will form into a ball.
Knead on a lightly floured surface until smooth and elastic and springs back when lightly pressed with two fingers, about 6 to 8 minutes. Cover with a towel; let rest for 10 minutes. (Resting allows the dough to loosen and be manageable.)
For the Parker House Dinner Rolls: Roll dough into a large 9×12-inch rectangle about ½″ thick.
Using a bench scrape or pizza cutter, cut 4 strips vertically about 3 inches wide. Rub softened butter on the left half of the strip.
Cut each strip horizontally 3 times so you have 12 squares. Fold the un-buttered half of each square overlapping the buttered side of each square and place rolls in a greased 9×13-inch or square baking dish.
Cover the pan with a towel and let dough rise until double in size about 30 minutes to an hour depending on how warm your kitchen is.
Bake at 375 degrees Fahrenheit for 20 to 30 minutes or until golden brown. Brush with additional butter, if desired. Serve warm.