Place the flour, 3/4 teaspoon of salt, and the butter in the bowl of a food processor fitted with the steel blade and pulse 12 to 14 times, until the butter is the size of peas. With the processor running, pour the vinegar and ice water through the feed tube and continue to process and pulse until the dough just comes together. Dump out on a floured board, form into a disk, wrap in plastic, and chill for 30 minutes.
Meanwhile, place the zucchini in a colander set over a plate. Toss it with 2 teaspoons of salt and set aside for 30 minutes. Spread the zucchini out on a clean dish towel, roll it up, and squeeze gently to remove some of the liquid. Put the zucchini slices into a bowl and toss with 1 tablespoon of olive oil. With a fork, mash together the goat cheese, thyme, lemon zest, 1/2 teaspoon salt, and 1/4 teaspoon pepper and set aside.
Preheat the oven to 400 degrees F. Roll the dough out on a floured board to an 11-inch circle and place on a sheet pan lined with parchment paper. Spread the dough with the goat cheese mixture, leaving a 1/2-inch border. Lay the zucchini slices in tightly overlapping circles, starting at the very edge of the pastry (the zucchini will shrink when it bakes). Continue overlapping circles of zucchini until the whole tart is covered. Drizzle with the remaining tablespoon of olive oil and sprinkle with pepper. Bake for 40 to 50 minutes, until the dough is golden brown. Cut in wedges and serve hot, warm, or at room temperature.
"Cooking for Jeffrey" by Ina Garten © Clarkson Potter 2016. Provided courtesy of Ina Garten. All rights reserved.