BAKE THE DOUGH for the crust: Preheat the oven to 400 degrees and line a half sheet pan with parchment paper. Roll the chilled dough out on a well-floured counter until it’s 11”x 7”. Gently roll the dough back onto the rolling pin and roll it back out onto the lined sheet pan. If it’s a bit too big, trim a little off; it doesn’t have to fit perfectly. There’s no need to pinch or flute the edges. Place another half sheet on top of the dough and bake for 15 minutes on a middle rack. (Alternately, line with foil and fill with dry beans before baking.) Remove the pans from the oven and take the top pan off. Using a fork, pierce the pastry all over (maybe 30 times) to keep it from puffing up. Bake another 8 minutes or until light brown, checking and piercing again any spots that puff up. Cool on rack 15 minutes. Brush all over with the 6 tablespoons Dijon-style mustard. Lower the oven temperature to 375 degrees F.
MAKE THE SAUCE IN THE FOOD PROCESSOR: Add all of the sauce ingredients (parsley – red pepper) except the olive oil to the work bowl fitted with a steel blade. Pulse until minced. With machine running, pour in the olive oil slowly until well-combined. (Alternately, chop finely on the board with a chef’s knife and whisk together in a large measuring cup.)
ADD THE VEGETABLES except the olives and green onions to a large bowl and drizzle the sauce over them. Gently combine.
SPRINKLE THE DIJON-COVERED CRUST WITH all the grated Gruyère except for ½ cup, which you’ll reserve for a topping. Sprinkle the Gruyère with the ½ cup of grated Parmigiano-Reggiano. Layer the sauced vegetables evenly over the cheese, carefully first straining out extra liquid from the bowl if necessary. Add any extra garlic and herb mixture over the vegetables. Make sure the vegetables are distributed evenly across the tart, not leaving all the peppers in one place, for instance. Sprinkle with the reserved ½ cup of grated Gruyère and the other 2 tablespoons of Parmigiano-Reggiano.
BAKE the tart for 20 minutes at 375 degrees F on the center rack. Remove tart from the oven and sprinkle evenly with reserved sliced Kalamata olives and green onions. Return the oven and bake another 10 minutes or until crust is crispy and toppings are bubbly. If fat from sauce and cheese has escaped into the pan, gently tip the pan with one hand, and carefully soak it up with a wad of paper towels in the other hand. Cool for a few minutes before cutting and serving hot, warm, or at room temperature. Best the day it's made, you can wrap tart leftovers tightly, store in the refrigerator, and serve cold within a day. Do not freeze.