Prep the tomatoes: Slice tomatoes and lay them on a paper towel–lined tray. Sprinkle with 1 teaspoon kosher salt. Let sit 20–30 minutes to draw out excess moisture. Gently blot the tops dry.

Make the dough: In a bowl, whisk flour, salt, and sugar. Cut in the cold butter with a pastry cutter or your fingertips until pea-sized bits form. Drizzle in ice water, 1 tablespoon at a time, tossing until the dough just holds together when pressed.

Chill: Press dough into a disk, wrap, and refrigerate for 30–45 minutes. This keeps the crust flaky and easier to roll.

Heat the oven: Preheat to 400°F (200°C). Line a baking sheet with parchment paper.

Roll it out: On a lightly floured surface, roll the dough into a 12-inch circle, about 1/8 inch thick. Transfer to the prepared baking sheet.

Build the base: Spread a thin layer of Dijon over the center, leaving a 2-inch border. Sprinkle the shredded cheese evenly over the mustard. The cheese helps create a moisture barrier so the crust stays crisp.

Layer the tomatoes: Arrange tomato slices in slightly overlapping circles over the cheese. Season with pepper and a pinch more salt if needed. Drizzle with olive oil and scatter the minced garlic.

Fold and finish: Fold the edges of the dough up and over the tomatoes, pleating as you go. Brush the crust with beaten egg. Sprinkle Parmesan over the exposed tomatoes and crust.

Bake: Bake for 35–45 minutes, until the crust is deep golden and the tomatoes are bubbling gently. Rotate the pan halfway through for even browning.

Rest, then garnish: Let the galette cool for 10–15 minutes. Top with torn basil and a pinch of flaky sea salt. Slice and serve warm or at room temperature.