1. Prebake the pie shells (see Note).

2. Peel the eggplant and cut it into ½-inch cubes. Toss the cubes together with the 2 teaspoons salt in a bowl. Let stand until some of the eggplant juices are drawn out, about 30 minutes.

3. Meanwhile, heat 1 tablespoon of the oil in a large skillet over medium heat. Add the onion and cook, stirring, until the onion is lightly browned and softened, about 8 minutes. Scoop the onion out of the pan into a bowl. Add the zucchini (and a little more oil if there isn’t enough to coat the bottom of the pan), cut side down, to the pan and cook, turning as necessary, until all cut sides are browned, about 10 minutes. (Browning the zucchini quarters before cutting them into cubes is easier than trying to brown all sides of the little cubes.) Cut the zucchini crosswise into ½-inch pieces and add to the bowl with the onion. Remove the pan from the heat while you tend to the eggplant.

4. Blot the eggplant dry as thoroughly as possible. Turn the heat to medium-low. Add the remaining oil to the pan and swirl to coat the bottom. Add the eggplant and cook, stirring often, until the eggplant is browned on most sides, about 10 minutes. The eggplant should be tender to the bite but not mushy. Scrape into the bowl with the onion and zuke. Crumble the thyme into the bowl and season the vegetables to taste with salt and pepper, remembering that the eggplant has been salted already. Let cool to tepid. The shells and vegetable mix can be prepared up to several hours before baking the quiches and held at room temperature.

5. When ready to bake the quiches, preheat the oven or reduce the oven temperature to 350°F.

6. Make the custard: Beat the cream, eggs, ½ teaspoon salt, the nutmeg, and pepper to taste together until smooth. Scatter a thin, even layer of cheese over the bottoms of both prebaked shells. Divide the vegetable mix between the 2 shells, spreading it evenly over the cheese. Top with the remaining cheese. Put the quiches on a baking sheet large enough to hold them both comfortably and pour the custard into the shells. Decorate the tops with the tomato halves, cut side up. Bake until the edges of the custard are set and the center is only slightly jiggly, about 45 minutes.

7. Let the quiches cool for at least 15 minutes before serving. Serve warm or at room temperature. The quiches can be made the day before and refrigerated. Rewarm in a 300°F oven for 15 to 20 minutes before serving.

Note: To prebake the pie shells, preheat the oven to 425°F. Poke the bottoms of the shells all over with a fork. Line the shells with parchment paper or aluminum foil. Fill halfway with pie weights, uncooked rice, or dried beans. Bake the shells for 20 minutes. Remove from the oven and let cool. Reduce the oven temperature to 350°F if you are baking the quiches right away; if not, turn the oven off.