Step 1

Preheat oven to 400°F. Place tomato slices on half of a parchment-paper lined baking sheet. Drizzle with 1 tablespoon of the oil, and sprinkle with 1/4 teaspoon of the salt. Toss together eggplants, zucchini, shallot, bell peppers, vinegar, and remaining 1 tablespoon oil in a bowl; spread evenly on opposite half of prepared baking sheet. Sprinkle eggplant mixture with 3/4 teaspoon of the salt and 1/8 teaspoon of the black pepper. Roast in preheated oven until vegetables are tender and beginning to brown, about 30 minutes. Cool 10 minutes.

Step 2

Increase oven temperature to 425°F. Place puff pastry sheet on a lightly floured work surface, and roll into a 14- x 10-inch rectangle. Lightly brush a 1/4-inch border with water, and fold border up and over to create a raised edge. Place dough rectangle on a baking sheet coated with cooking spray. Poke holes all over bottom of dough with a fork. Sprinkle bottom of dough evenly with goat cheese and 1 teaspoon of the thyme. Bake at 425°F until lightly browned, about 12 minutes.

Step 3

Top crust evenly with tomato slices in a single layer, and top evenly with eggplant mixture. Sprinkle evenly with remaining 1/4 teaspoon salt and 1/8 teaspoon black pepper. Return to oven, and bake until pastry is golden brown, 4 to 6 minutes. Transfer baking sheet to a wire rack, and cool until crust is set, about 10 minutes.