(Makes 16 rolls.) Generously grease large bowl and 10-inch round baking pan. Scald milk with 1 tablespoon butter and cool to lukewarm. Sprinkle yeast over warm water in large bowl and let stand until proofed and foamy, about 10 minutes. Stir in milk, sugar and salt. Add 2 cups flour and beat well. Add 1 more cup flour and mix thoroughly.

Turn out onto lightly floured board and knead in remaining flour until dough is smooth and satiny, about 10 minutes. Place in greased bowl, turning to coat entire surface. Cover and let rise in warm area until doubled, 1 1/2 hours.

Saute onion in butter until tender but not browned, set aside. Punch dough down and knead several times. Roll into 16x11-inch rectangle. Sprinkle evenly with onion, then with dillweed. Roll lengthwise jelly roll fashion. Slice into 1-inch pieces and arrange in prepared 10-inch pan so each roll barely touches. Brush with butter and let rise until doubled, 30 to 45 minutes.

Preheat oven to 375 deg. Bake rolls until golden brown, about 30 minutes.