PREPARE THE TART DOUGH. If you are using unyeasted crust, partially prebake it. Halve the peppers lengthwise, remove the seeds and veins, then halve them crosswise and slice very thinly.
Warm 2 tablespoons of the olive oil in a wide pan, add the peppers, onion, half the garlic and 1/4 teaspoon salt. Saute over medium-high heat for several minutes, then lower the heat, add the water or white wine, cover and stew until the peppers and onion are very soft and sweet.
If the peppers and onion threaten to stick as the sugars are released, add additional small amounts of water or wine. Taste for salt, and season with freshly ground black pepper when the peppers and onion are finished cooking.
Put 2 tablespoons of the olive oil in a blender jar with the remaining garlic and a few of the basil leaves and puree. Gradually add the rest of the basil leaves, using more oil if necessary. Scrape the puree out of the jar, stir in the Parmesan or Romano cheese and season with salt.
If using the yeasted tart dough, prepare the shell, then make the custard. Beat the eggs and yolks together, then add the cream, 1/2 teaspoon salt and pepper. Preheat the oven to 400F.
Paint the crust with the basil puree, then lay half the grated Provolone cheese on top, followed by the peppers and onion, and the olives.
Add the remaining cheese, then the custard. Bake the tart in the center of the oven until it is golden brown, and set, 35 to 40 minutes. Let the tart rest 5 to 10 minutes before serving.