Mix butter, garlic, and 2 tablespoons of the parmesan cheese.
On a lightly floured board, pat, roll, and stretch dough into a 12- by 16-inch rectangle. If dough springs back, let rest a few minutes, then continue to shape.
Spread garlic-butter mixture evenly over dough. Sprinkle with 1/3 cup cheddar cheese.
From a 16-inch edge, roll dough to enclose filling. Cut log of dough crosswise into 16 equal rolls.
Setting on cut sides, evenly space rolls in a buttered 9- by 13-inch pan.
Cover pan lightly with plastic wrap. Let rolls rise in a warm place until almost doubled in size, 25 to 35 minutes. Remove wrap; sprinkle rolls with remaining parmesan and cheddar cheeses.
Bake in a 350° oven until golden brown, 30 to 35 minutes. Let cool in pan on a rack about 5 minutes. With a wide spatula, lift rolls from pan and serve warm or cool.
Nutritional analysis per roll.