Pour 1 cup warm water into a medium bowl; add sugar and sprinkle with yeast. Let stand until foamy, 5 minutes.
Whisk oil and 1 teaspoon salt into yeast mixture. Add flour and stir with a wooden spoon until liquid is incorporated (dough will appear dry). Turn out onto a floured work surface. Knead until dough comes together in an elastic ball, 2 minutes. Transfer to an oiled medium bowl; brush lightly with oil. Cover bowl with plastic wrap; set in a warm, draft-free place until dough has doubled in bulk, 45 minutes. Punch down dough and cover; let rise another 30 minutes.
Turn out dough onto a lightly floured work surface. Divide into 4 equal pieces. Let rest 15 minutes before using.
To store, refrigerate dough pieces, covered, up to 2 days.