Dissolve sugar and yeast in warm water in a large bowl; let stand 5 minutes. Add oil and egg, stirring with a whisk. Lightly spoon flour into dry measuring cups; level with a knife. Add flour and salt to yeast mixture; beat with a mixer at medium speed until smooth.
Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes). Place 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 dough. If indentation remains, the dough has risen enough.)
Punch dough down; shape into a ball. Return dough to bowl; cover and let rise 1 hour or until doubled in size.
Punch dough down; turn dough out onto a lightly floured surface. Cover and let rest 15 minutes.
Divide dough into 3 equal portions. Working with 1 portion at a time (cover remaining dough to keep from drying), shape each portion into a 15-inch rope. Place ropes lengthwise on a baking sheet coated with cooking spray (do not stretch); pinch ends together at one end to seal. Braid ropes, and pinch loose ends together to seal. Cover and let rise 1 hour or until doubled in size.
Preheat oven to 375°.
Uncover dough. Combine 2 teaspoons water and egg yolk; brush over braid. Bake at 375° for 35 minutes or until loaf is browned on bottom and sounds hollow when tapped. Remove from pan; cool on a wire rack.