For the All-butter Crust

1. In a large mixing bowl, whisk together the flour and kosher salt.
2. Scatter the cold butter pieces evenly over the flour.
3. Using a pastry cutter, cut the butter into the flour until the mixture resembles coarse crumbs with pea-sized pieces of butter remaining.
4. Start with 2 tablespoons of ice water. Using a silicone spatula, gently fold the dough together, adding additional ice water 1 tablespoon at a time until the dough easily comes together and picks up the loose, sandy bits of flour. Depending on the humidity, you may need anywhere from 2 to 6 tablespoons.
5. Gather the dough into a disk without kneading. Wrap tightly in plastic wrap.
6. Refrigerate for at least 1 hour before rolling.

For the Galette

1. While the dough chills, arrange the halved tomatoes, cut side up, on a baking sheet or tray lined with paper towels. Lightly sprinkle the cut surfaces with kosher salt and let them rest for about 20 minutes to release some of their moisture.
2. Gently blot the cut surfaces of the tomatoes with paper towels to remove the collected moisture. Do not add additional salt.
3. Preheat the oven to 400°F. Line a large baking sheet with parchment paper.
4. On a lightly floured surface, roll the chilled dough into a roughly 13-inch circle. Don’t worry about making it perfectly round; the irregular shape is part of the galette’s rustic character.
5. Transfer the dough to the parchment-lined baking sheet. Scatter the mozzarella evenly over the dough, leaving about a 1½-inch border around the edge.
6. Arrange the baby spinach in a light, even layer over the mozzarella. Separate the thinly sliced red onion into individual arcs and scatter them evenly over the spinach.
7. Arrange the tomatoes over the spinach and onion, mostly cut-side up, generously covering the filling. Depending on the size of the tomatoes, you may not need all of them.
8. Lightly grate the Parmigiano-Reggiano over the tomatoes, then add a restrained amount of coarsely ground black pepper.
9. Fold the uncovered edge of the dough over the filling, working your way around the galette and letting the dough overlap naturally as you go.
10. Whisk together the egg and 1 tablespoon water. Lightly brush the egg wash over the exposed pastry.
11. Bake for about 30–35 minutes, or until the crust is deep golden brown, the tomatoes have softened and begun to caramelize, and the bottom of the galette is fully baked.
12. Let the galette cool on the baking sheet for about 15–20 minutes before slicing and serving.