Combine yeast, warm water, and 1 teaspoon sugar in a 1-cup liquid measuring cup; let stand 5 minutes. Combine remaining sugar, milk, oil, and salt in a small saucepan; cook over medium heat until sugar dissolves, stirring occasionally. Cool to 115°. Add yeast mixture to milk mixture, stirring well with a wire whisk.
Place 6 cups flour in a large bowl. Gradually add liquid mixture to flour, stirring to make a stiff dough. Place dough in a large bowl coated with cooking spray, turning to coat top. Let stand at room temperature 10 minutes. Cover and refrigerate at least 8 hours. (Dough may remain in refrigerator up to 5 days.)
To make rolls, sprinkle remaining 1 tablespoon flour over work surface. Punch dough down; turn out onto floured surface, and knead 2 or 3 times. Divide dough into thirds. Working with 1 portion at a time, shape dough into 12 balls. Place balls in a 9-inch round cakepan coated with cooking spray. Repeat procedure with remaining portions of dough.
Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in bulk. Bake at 400° for 10 to 12 minutes or until golden. Coat rolls lightly with cooking spray.