In a large bowl, combine sugar, salt, yeast and 2 1/4 cups flour. In 2 quart saucepan over low heat, heat water and 1/2 cup butter until very warm (120 to 130 F). (Butter does not need to melt.)
With mixer at low seed, gradualy beat liquid into dry ingredients. Add egg, increase speed to medium; beat 2 minutes occasionally scraping bowl with rubber spatula. Beat in 3/4 cup flour or enough to make a thick batter; continue beating 2 minutes, scraping bowl wih rubber spatula. Stir in 2 1/2 cups flour to make a soft dough.
Turn dough onto lightly floured surface and knead until smooth and elastic, about 10 minutes. Shape into ball; place into greased large bowl, turning over to grease top. Cover with towel; let rise in warm place, until doubled, about 1 1/2 hours.
Punch down dough. Turn dough over; brush with oil. Cover bowl tightly with plastic wrap and refrigerate at least 2 hours or until ready to use, punching down dough occasionally.
About 2 1/2 hours before serving: Grease 15 1/2" by 10 1/2" open roasting pan. Cut dough into 30 equal pieces; shape into balls and place in pan. Cover with towel; let rise in warm place, away from draft, until doubled, abut 1 1/2 hours.
Preheat oven to 400 degrees. Bake rolls 15-20 minutes until golden brown. Brush rolls with softened butter. Remove from pan and serve hot.