In a food processor, pulse flour and salt to combine. Add cold butter and pulse until mixture resembles coarse meal with some pea-sized pieces remaining, about 10 one-second pulses.

Drizzle 4 tablespoons ice water over flour mixture and pulse just until dough starts to come together, 3 to 5 pulses. If dough feels dry, add more water 1 teaspoon at a time. Turn out onto plastic wrap, press into a disk, wrap tightly, and refrigerate at least 1 hour or up to 2 days.

Lay tomato slices on paper towels, sprinkle lightly with kosher salt, and let drain 15 minutes. This prevents a soggy crust. Pat dry before using.

In a small bowl, mash goat cheese with minced garlic, thyme leaves, 1 tablespoon olive oil, and honey until spreadable. Season with black pepper.

Preheat oven to 400F. Roll chilled dough on parchment paper to a 12-inch circle, about 1/8 inch thick. Transfer parchment to baking sheet. Spread goat cheese mixture over dough, leaving a 2-inch border. Arrange tomato slices over cheese, overlapping slightly. Fold dough edges over tomatoes, pleating as you go. Brush folded crust with remaining 1 tablespoon olive oil.

Bake 35 to 40 minutes, until crust is deep golden and tomatoes are softened with some caramelized edges. Cool on baking sheet 10 minutes. Sprinkle with flaky sea salt and fresh thyme sprigs. Serve warm or at room temperature.