Combine 1 1/2 cups flour, yeast, sugar, and garlic salt in a large mixing bowl; stir well.
Combine milk and 3 tablespoons butter in a small saucepan; cook over medium heat 2 to 3 minutes or until butter melts. Cool to 100° to 110°.
Gradually add milk mixture to flour mixture, beating well at medium speed with an electric mixer. Add egg, beating well. Add rice and 1/2 cup Parmesan cheese; beat well. Using a wooden spoon, gradually stir in enough remaining flour to make a soft dough.
Turn dough out onto a lightly floured surface, and knead until smooth and elastic (about 6 to 8 minutes). Shape dough into a ball; place in a well-greased bowl, turning to grease top. Cover.
Turn oven to 200° for 1 minute; turn oven off. Place dough in oven; let rise 15 minutes.
Punch dough down; turn out onto a lightly floured surface, and knead lightly 4 or 5 times. Divide dough into 16 pieces; shape into balls. Dip tops of balls into melted butter; dip into remaining 1 cup Parmesan cheese. Arrange balls on a greased 15" x 10" jellyroll pan; let rest 5 minutes.
Bake at 375° for 18 minutes or until lightly browned.