Using a mandoline or a very sharp knife, cut the tomatoes, onions, eggplant, yellow squash and zucchini into very thin slices, about ⅛-inch thick. (Cut the tomatoes and onions parallel to the equator.)

Line several large sheet pans with towels; reserve one pan for assembling the galette, below. Place the sliced vegetables on top, and lightly sprinkle with salt on both sides to draw out moisture. Cover with more towels to absorb the released juices. (To avoid using so many pans, you can double up layers of sliced vegetables if you use clean dish towels or a double layer of paper towels in between.) Let the vegetables sit for about 30 minutes to draw out the maximum moisture.

While the vegetables rest, position a rack in the middle of the oven and preheat to 375 degrees. Now is also a good time to make the goat cheese filling and prep the puff pastry.

In a small food processor, pulse together the goat cheese, cream cheese and garlic for 30 seconds to 1 minute, until the mixture begins to come together. Scrape down the bowl, and pulse again until the mixture is well combined and fluffy, another 30 seconds to 1 minute. (Alternatively, in a large bowl, beat the mixture with a flexible spatula.) Scrape the mixture into a small bowl and fold in the chopped herbs.

Place a large sheet of parchment paper on the counter and dust it with flour. Set the puff pastry on the parchment, lightly dust with more flour, and roll it into a 12-by-14-inch rectangle. Slide the parchment paper with the pastry onto an empty sheet pan.

With the tip of a sharp paring knife, score an approximately 1-inch border around the pastry, being careful not to cut all the way through. Gently poke the inside of the rectangle with the tines of a fork, evenly and all over. This will prevent this area from rising while the tart bakes so you get a clean border.

Using a butter knife or a small offset spatula, spread the mustard in a thin layer across the inner section of the pastry, taking care not to go over the border. Then spread the goat cheese mixture over the mustard, taking care not to go over the border.

In a small bowl, whisk together the egg and water until combined, and brush the border of the tart with it.

Assemble the tart by shingling the vegetables in rows, layering them in an overlapping pattern like just-fallen dominos. Use any order you like, but we followed a pattern of tomato, yellow squash, zucchini, red onion, eggplant. We do, however, recommend alternating which side you start each row. The number of rows and slices you use will vary depending on the size of the vegetables, but expect 3 or 4 rows, using 15 to 20 slices of each type of vegetable total. (See Notes for tips on using extras.)

Once you are satisfied with your design, drizzle the vegetables with oil and sprinkle lightly but evenly with salt. Bake for 50 to 60 minutes, or until the pastry is deep golden brown and the vegetables visibly shrink and are cooked. If the pastry edges start to get too dark, loosely tent the crust with foil. Transfer to a wire rack and let cool for about 10 minutes before serving, or let cool completely and serve at room temperature.