Start by mixing flour and salt, then pulse with cold butter until crumbly. Add ice water and vinegar, and gently bring the dough together. Shape into a disk and refrigerate for at least 2 hours to keep it firm and flaky.
Slice the tomatoes and sprinkle them with salt. Let them sit for about 30 minutes so excess moisture releases. This step prevents a soggy crust and keeps the galette crisp.
In a bowl, mix goat cheese with olive oil, garlic, chives, thyme, lemon zest, and pepper. Stir until smooth and creamy. This layer adds richness and prevents the crust from getting wet.
Take chilled dough and roll it into a 12-inch circle on a floured surface. Keep it about ⅛-inch thick for even baking. Transfer carefully onto a lined baking sheet.
Spread the cheese mixture in the center, leaving a border around the edges. Arrange tomato slices on top in layers. Fold the edges over the filling to create a rustic shape.
Brush the edges with egg wash and bake at 400°F (200°C) for 40–45 minutes until golden brown. Let it cool for 10 minutes before slicing, then garnish with fresh basil and serve.