To prepare crust, dissolve yeast and honey in warm water in a large bowl; let stand for 5 minutes. Lightly spoon flours into dry measuring cups, and level with a knife. Stir 1 cup bread flour and 1 tablespoon oil into yeast mixture. Cover and let rise in a warm place (85°), free from drafts, 1 1/2 hours or until bubbly. Stir in 1/2 cup bread flour, whole wheat flour, and 1 teaspoon salt.
Turn dough out onto a floured surface. Knead until smooth and elastic (about 10 minutes); dough will feel tacky. 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, for 1 hour or until doubled in size. (Press two fingers into the dough. If indentation remains, the dough has risen enough.) Punch dough down; cover and let rest 10 minutes.
To prepare the topping, heat 1 tablespoon oil in a 12-inch nonstick skillet coated with cooking spray over medium-high heat. Add onion, and cook for 5 minutes, stirring frequently. Stir in 1 teaspoon salt, thyme sprigs, garlic, and bay leaves; cook for 15 minutes or until deep golden brown, stirring frequently. Remove from heat. Discard thyme sprigs and bay leaves.
While onion is cooking, cut bell peppers in half lengthwise, discarding seeds and membranes. Place the pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil for 15 minutes or until blackened. Place in a zip-top plastic bag, and seal. Let stand for 15 minutes. Peel and coarsely chop.
Preheat oven to 425°.
Roll the dough into a 12 x 8-inch rectangle. Place the dough on a baking sheet coated with cooking spray. Top with the onion mixture and the chopped bell pepper. Sprinkle with black pepper. Bake at 425° for 25 minutes or until the crust is golden brown. Cool slightly. Sprinkle with chopped thyme. Cut into 8 squares, and cut each square in half diagonally. Garnish with thyme sprigs, if desired.