Chop one of the onions. In a covered frying pan, cook the onion and garlic in 2 tablespoons olive oil over low heat until very tender. Chop one of the red peppers and add to the pan. Continue cooking until the pepper is fork- tender and limp. Puree the onion-pepper mixture in a blender or food processor and set aside.
Cut another pepper into fine dice. In a large bowl, dissolve the yeast in warm water. Add sugar, salt, cayenne, saffron, several grinds of fresh pepper, onion-pepper puree and diced raw pepper.
Stir in 3 cups flour, or enough to form a soft dough that can be turned out onto a floured surface. Knead for 10 minutes, adding flour until the dough is firm. Place in a oiled bowl, cover with a towel and let rise in a warm spot for 1 hour.
While the bread rises, cut the remaining onion into slices 1/2-inch thick. Separate the rings and cook them in the remaining 2 tablespoons of olive oil over low heat until almost tender. Cut the remaining red pepper into strips. Add to the onion and cook until tender. Let cool.
Take the dough from the bowl and shape it into a flat round on an oiled baking sheet. Press or roll the dough out to a circle about 10 inches in diameter. Press down on the center of the dough slightly and make a 9-inch central portion indented just a bit to receive the topping.
Mix the egg and oregano into the cooked vegetables. Spread the mixture over the indented portion of the bread, arranging the pepper artistically in the process. Sprinkle with salt and grind on a bit of pepper. Let the bread rise for 30 minutes.
Heat oven to 350 degrees. Bake until bread sounds hollow when tapped on the bottom, about 45 to 50 minutes. Cool on a wire rack.