STIR YEAST AND SUGAR into warm water; let stand until foamy, about 5 minutes. Put both flours, salt and oil into food processor work bowl fitted with metal blade. Turn processor on to combine mixture. With processor running, slowly add yeast mixture. Mix until dough cleans sides of bowl. If dough is too sticky, add more flour by the tablespoon, working it in before adding more. If dough is too dry and crumbly, add more water by the teaspoon, working it in before adding more. Once desired consistency is reached, process dough until well kneaded, uniformly supple and elastic, about 40 seconds. Add walnut pieces and process for 10 seconds. Remove blade. Then remove dough from bowl and press all loose walnuts into it.
Transfer dough to large plastic bag, squeeze out air and seal at top. Place dough in bowl. Let rise in warm spot until doubled, about 1 hour. Oil baking sheet. Punch dough down and shape into smooth ball. Place round side up on baking sheet. Cover loosely with oiled plastic. Let rise in warm spot until doubled, about 1 hour. 15 minutes before baking, preheat oven to 400F, with rack in center of oven. When loaf has doubled, slash loaf for surface design. Lightly brush with glaze. Bake until loaf is deeply browned and sounds hollow when rapped on the bottom, about 35 minutes. Immediately remove from pan to cool on rack.
NOTE: (To toast nuts, spread single layer on jelly roll pan and bake in 350F oven until fragrant and toasted, 8-to-10 minutes, watching carefully to avoid burning) Makes 1 Loaf