Make the tart shell: In a large bowl mix the flour and salt. With a pastry blender, cut in the butter until the mixture resembles coarse, fresh breadcrumbs. In a small dish, lightly beat the egg yolk with 2 Tbs. cold water. Drizzle it over the flour mixture and stir with a fork until the egg is evenly distributed. With the fork, stir in 2 to 4 Tbs. cold water, 1 Tbs. at a time, until the dough starts gathering into clumps. If you press some of the dough between your fingers, it should hold together. Dump the dough onto a counter. Gently press and gather the dough together, shaping it into a disk. Wrap in plastic wrap and chill for at least 1 hour.
Roll the chilled dough on a lightly floured surface into a circle 3/16 inch thick and 12 to 13 inches in diameter. Drape the dough over your rolling pin and lift it over a 9-1/2-inch fluted tart pan with a removable bottom. Unroll the dough and gently press it into the pan without stretching it. Then pass the rolling pin over the rim to cut off the excess dough. Wrap and freeze for at least 30 minutes.
Position a rack in the center of the oven and heat the oven to 375°F. Line the chilled tart shell with foil and fill it with dried beans or pie weights. Let the excess foil stand straight up, rather than folding it over the edges of the pan. Bake until the pastry edges are light golden, about 30 minutes. Carefully remove the foil and weights. Bake until the base of the pastry is beginning to turn golden, about 10 minutes more. If the pastry puffed at all, gently press down the bubbles before cooling completely on a rack.
Make the filling: Position a rack in the center of the oven and heat the oven to 400ºF.
Put the peppers on a rimmed baking sheet and roast in the oven, turning every 15 minutes until browned and wrinkled all over, 45 to 60 minutes. Remove the peppers from the oven, cover with a dishtowel, and set aside to cool. Turn the oven down to 375°F.
Seed, peel, and cut the peppers into wide strips or bite-size pieces. Set aside. Heat the olive oil in a 10-inch skillet over medium heat. Add the onion, half the thyme, 1/2 tsp. salt, and 1/4 tsp. pepper and cook, stirring frequently, until the onions are very soft and golden brown, 15 to 20 minutes. Reduce the heat to medium low or low if it looks like they're burning. Set aside at room temperature to cool.
In a small bowl, whisk the cream, eggs, and 1/4 tsp. each salt and pepper. In a medium bowl, mix the peppers, onions, prosciutto, basil, parmigiano, and remaining thyme.
Put the tart shell on a baking sheet. Distribute the pepper mixture in the tart shell and scatter the goat cheese over it. Slowly drizzle the egg mixture over the filling until it reaches the rim of the pastry (you may not need it all). Bake the tart until the custard is set, 30 to 35 minutes. Cool on a rack and serve warm or at room temperature.