Preparation

Make the dough

• In the bowl of a food processor, combine the flour and salt. Pulse briefly to combine. Add the butter. Pulse quickly about twenty times, or until the butter particles are quite small (like tiny pebbles). With the motor running, add the ice water in a steady stream. (This will take about 10 seconds.) Stop the motor. Then pulse quickly six or eight times, just until the mixture begins to leave the sides of the bowl and clump together. The mixture wlil still be somewhat loose and crumbly. That’s okay; you will bring the dough together in the next step.
• Turn the mixture out into a big mixing bowl and knead it briefly against the sides of the bowl to finish bringing it together as a dough. Once you have incorporated all the crumbs, knead once or twice to smooth it out just a bit. While you don’t want to overhandle the dough, you also don’t want to be afraid to handle it as much as you need to in order to bring all the bits of the dough together, as it will ultimately be easier to roll out.
• Divide the dough in half. If you have a scale, you can weigh the dough pieces to make sure they’re of equal or close-to-equal weight. They should each weigh about 9-1/2 oz.
• Shape each piece into a disk about 1 inch thick (and about 4 inches across). Again, don’t be afraid to handle the disk just enough to smooth out the cracks and make a tidy disk. Dust lightly with flour, wrap in plastic wrap, and refrigerate for at least 1 hour or up to 2 days.
• Remove one disk of dough from the fridge 45 minutes before rolling it (see leftovers note below about storing the extra disk of dough). Make the filling while the dough comes to room temperature.

Make the filling

• Preheat the oven to 400°F. Position a rack in the center of the oven. In a 13-by-9-inch heatproof glass baking dish (or two smaller shallow baking dishes with a total volume of about 3 quarts), combine the cherry tomatoes, bell pepper, eggplant, zucchini, red onion, olive oil, and 1/2 tsp. salt. Toss gently but thoroughly and spread in a single layer. Roast until the veggies have shrunk and caramelized but are still a bit moist, 45 to 55 minutes. Let cool in the baking dish.

Make the egg wash

• In a small bowl, whisk together the egg yolk and heavy cream, cover with plastic wrap, and set aside.

Assemble and bake the tart

• Be sure that one oven rack is still positioned in the center of the oven. Line a large heavy-duty rimmed baking sheet with parchment.
• Sprinkle your work surface lightly with flour and spread it around with your hand. Put the disk of dough in front of you and lightly tap it with the rolling pin to start softening and spreading it. Gently roll it out, lifting and giving the disk a quarter-turn after each roll, until you have a roughly 12-inch round. Try not to roll your pin over the edges of the dough, as that will tend to make the edges thinner than the center. (If your edges get very ragged or torn, it’s okay to patch them back together or trim them.) If the dough is sticking, lift it up and toss a bit of flour underneath it and/or over it. Roll up or drape the dough over your rolling pin, and unroll or undrape it onto the prepared baking sheet.
• Sprinkle 1 Tbs. of the Parmigiano over the dough, leaving a 2-inch border around the edge. Top the Parmigiano with half of the goat cheese, half of the mint, and half of the roasted filling, again leaving a 2-inch border. Sprinkle with 1 Tbs. of the Parmigiano, and repeat with the remaining goat cheese, mint, and filling. Top with 1 Tbs. of the Parmigiano.
• Pleat and fold the edges of the dough up and over the outer edge of the filling all the way around the tart. (You will be folding in that 2-inch border.) You don’t have to go crazy making a lot of pleats; folding in a piece of dough about every 2 to 3 inches around the tart will get you the results you want. (You’ll have a total of eight to ten pleats.)
• Brush the edges of the dough with some of the egg wash (you won’t use it all), and sprinkle the remaining 1 Tbs. Parmigiano over the edges as well as the rest of the tart.
• Bake until nicely golden all over and crisp and brown on the bottom (check with spatula), 38 to 40 minutes. Let cool for a few minutes and use the parchment to slide the tart onto a cutting board. Let cool for another 5 to 10 minutes before slicing and serving.

  

You can freeze the extra disk of dough, wrapped in plastic, for up to 4 weeks. Thaw it in the fridge overnight before using.