Combine 2 cups flour, sugar, salt, and yeast in a large mixing bowl; stir well. Combine milk and butter in a saucepan; heat until butter melts, stirring occasionally. Cool to 120° to 130°. Gradually add liquid mixture to flour mixture, beating well at low speed of an electric mixer. Beat an additional 2 minutes at medium speed. Add eggs and 3/4 cup flour, beating 2 minutes at medium speed. Gradually stir in enough of the remaining 4 1/2 cups flour to make a soft dough.
Sprinkle 1 tablespoon flour evenly over work surface. Turn dough out onto floured surface, and knead until smooth and elastic (about 8 to 10 minutes). Place dough in a large well-greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in bulk.
Punch dough down; divide in half. Divide each half into 11 equal portions; shape each portion into a ball. Place at least 1 inch apart on large greased baking sheets.
Cover and let rise in a warm place, free from drafts, 30 minutes or until doubled in bulk. Bake at 325° for 18 to 20 minutes or until lightly browned. Remove rolls from baking sheets; let cool on wire racks.