Dissolve the yeast and sugar in 1/4 cup warm water; let stand 10 minutes. Add 1/2 cup water, oil, and egg; stir with a whisk. Lightly spoon flour into dry measuring cups; level with a knife. Place flour and salt in food processor; pulse 2 times or until blended. With processor on, slowly add yeast mixture through food chute; process 20 seconds or until dough forms a ball. Process an additional minute. Place dough in a large bowl lightly coated with cooking spray; turn 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, reshape into a ball, and return to bowl; cover and let rise 1 hour or until doubled in size.
Punch dough down; turn out onto a lightly floured surface. Let rest 15 minutes. Divide dough into 3 equal portions; 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; pinch loose ends to seal. Cover and let rise 1 hour until doubled in size.
Preheat oven to 375°.
Combine 2 teaspoons water and egg yolk. Uncover dough; gently brush loaf with egg yolk mixture. Bake at 375° for 35 minutes or until loaf sounds hollow when tapped. Remove from pan; cool on a wire rack.