Position mixing blade in food processor bowl. Add 2 tablespoons warm water, yeast, and sugar; pulse once or twice. Scrape sides of bowl and let stand 3 minutes, until foamy. Add 1 cup flour, salt, oregano, and celery seeds.
With processor running, pour remaining 1/2 cup plus 2 tablespoons water through food chute. Pulse 1 minute or just until dough forms a ball and begins to pull away from sides of bowl. Add green onions, and pulse 6 times to blend onions into dough.
Place dough in a medium bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85 degrees F), free from drafts for 20 minutes or until doubled in bulk.
Punch dough down. Sprinkle remaining 2 tablespoons flour evenly over work surface. Turn dough out onto floured surface, and knead until smooth and elastic (about 5 minutes). Roll dough into a 14-inch log.
Carefully transfer to a baking sheet coated with cooking spray. Coat a sheet of plastic wrap with cooking spray, place lightly over loaf, coated-side down. Let rise 20 minutes.
In a small bowl combine egg white and 1 teaspoon water; beat at high speed of an electric mixer just until foamy. Brush evenly with egg white mixture.
Bake at 375 degrees F for 30 minutes or until loaf sounds hollow when tapped.
Transfer to a wire rack immediately, and cool completely. Cut into 8 slices.