In a bowl or food processor, combine 1.5 cups flour, 1/4 tsp salt and 1/2 tsp sugar. Cut or pulse in 6 tbs (3/4 stick) cold unsalted butter until mixture resembles coarse meal with some pea-size pieces. Sprinkle 3 tbs cold water over flour-butter mixture, tossing gently until the dough just comes together. If needed add up to 1 tbs more water. Do not overwork.

Form dough into a flat disk, wrap in plastic, and chill in refrigerator for at least 30 minutes (up to 2 hours). Chilling relaxes gluten and firms the butter for a flaky crust.

Preheat oven to 425°F (220°C). Line a baking sheet with parchment. On a lightly floured surface, roll chilled disk to about 11–12 inch round, roughly 1/8 inch thick. Transfer to parchment-lined sheet. Refrigerate for 10 minutes while preparing filling to keep dough cold.

Filling

Prepare tomatoes: slice heirloom tomatoes 1/4 inch thick. Place slices on a paper towel-lined tray or colander and lightly salt to draw out excess moisture for 10–15 minutes; blot any liquid. This prevents a soggy tart.

Finely mince 1 shallot and 1 garlic clove. In a small bowl combine 1 tsp Dijon mustard with 2 tbs olive oil, minced shallot, minced garlic, and 1 tsp chopped fresh thyme. Season mixture with 1/4 tsp coarse sea salt and 1/4 tsp black pepper; whisk to combine.

Spread: On the chilled rolled-out dough, leave a 1-inch border. Lightly brush the center area (inside border) with the mustard-olive oil mixture to create a flavorful seal and barrier against tomato juices.

Layer the goat cheese (4 oz, crumbled) evenly over the brushed area, leaving the 1-inch rim clear. Distribute the blotted tomato slices in a single layer, slightly overlapping, across the cheese. Tuck a few extra tomato pieces into gaps so coverage is even but not piled high.

Season tomatoes with remaining 1/4 tsp coarse sea salt (or flaky salt) and 1/4 tsp black pepper. Sprinkle the rest of the thyme leaves and the chiffonaded basil over the tomatoes. Drizzle 1 tbs olive oil lightly across the top.

Fold and crimp: Gently fold the exposed 1-inch pastry edge over the tomatoes, pleating as needed to form a rustic galette edge. Brush the folded rim with the lightly beaten egg to promote browning and sprinkle any remaining coarse salt on the crust edge.

Bake the tart on the parchment-lined sheet in the preheated 425°F (220°C) oven for 18–22 minutes, or until the crust is deep golden brown and the tomatoes are softened and slightly caramelized. If the crust browns too quickly, rotate the sheet or tent loosely with foil after 12–14 minutes.

Remove tart from oven and let rest on the sheet for 8–10 minutes to set juices. This keeps the filling from becoming runny when sliced.

Finish and garnish: After resting, scatter the remaining fresh basil (if any), microgreens if using, and drizzle 1 tsp extra-virgin olive oil over the tart. Serve warm or at room temperature in wedges.