Make the crust: Pulse the flour, cornmeal and fine salt in a food processor to combine. Add the butter and 3 tablespoons manchego; pulse until the mixture looks like coarse meal with pea-size bits of butter. Drizzle in 4 tablespoons ice water and pulse until the dough comes together; add 1 more tablespoon ice water if necessary. Turn out onto a sheet of plastic wrap and pat into a disk. Wrap and refrigerate until firm, about 45 minutes.

Put the dough between 2 sheets of parchment paper and roll into a 13-inch round. Transfer the dough to a 9 1/2-inch deep-dish pie plate. Fold the overhang under itself and crimp the edges. Pierce the bottom of the crust all over with a fork. Refrigerate until firm, about 20 minutes. Meanwhile, preheat the oven to 350 degrees F.

Line the crust with foil, then fill with dried beans. Bake until the edges are golden, about 20 minutes. Remove the foil and beans and continue baking until golden all over, 10 to 15 more minutes. Transfer to a rack to cool.

Make the filling: Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the onion and cook, stirring, until golden, about 15 minutes. Let cool. Meanwhile, thinly slice the tomatoes; toss with 1 teaspoon kosher salt in a colander. Let drain, gently tossing occasionally, about 30 minutes.

Increase the oven temperature to 375 degrees F. Combine the remaining 3/4 cup manchego, the mozzarella, mayonnaise, breadcrumbs, 2 tablespoons each chives and parsley, the thyme, 1/4 teaspoon each kosher salt and pepper, and the sauteed onion in a bowl. Spread in the crust. Arrange the tomatoes on top. Drizzle with the remaining 1 tablespoon olive oil and season with pepper. Bake until the tomatoes are browned, about 50 minutes. Top with the remaining 1 tablespoon each chives and parsley.

Photograph by Con Poulos