Dissolve sugar and yeast in warm water in a large bowl; let stand 5 minutes. Lightly spoon flour into dry measuring cups, and level with a knife. Add 2 3/4 cups flour, oil, and salt to yeast mixture; stir until blended. Turn the dough out onto a floured surface. Knead until smooth and elastic (about 10 minutes); add enough of the remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel tacky).
Place the dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size. (Press two fingers into the dough. If indentation remains, the dough has risen enough.) Punch dough down; cover and let rest for 5 minutes. Divide dough in half. Shape dough according to recipe directions.