Add the flour, salt, black pepper, thyme, basil, and Parmigiano Reggiano to the bowl of a food processor. Pulse 2–3 times to combine.

Scatter the cold butter over the dry ingredients. Pulse 8–10 times until the mixture resembles coarse meal, with some pea-sized bits of butter remaining.

With the processor running, slowly drizzle in cold water through the feed tube. Stop as soon as the dough begins to clump together.

Turn the dough out onto a lightly floured surface, shape into a disc, and wrap in plastic wrap. Refrigerate for at least 30 minutes.

Arrange the tomato slices in a single layer on a cutting board lined with paper towels. Sprinkle with salt and let sit for 15 minutes to draw out excess moisture. Pat dry.

In a small bowl, stir together the ricotta, garlic, lemon zest, torn basil leaves, dried oregano, and 2 tablespoons of the grated Parmigiano Reggiano.

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

On a lightly floured surface, roll out the chilled dough into a 12-inch circle. Transfer dough to the prepared baking sheet.

Spread the ricotta mixture over the center of the dough, leaving a 2-inch border around the edges.

Arrange the tomato slices over the ricotta, slightly overlapping. Drizzle with olive oil and season with black pepper and red pepper flakes.

Sprinkle the remaining ¼ cup (4 tablespoons) of Parmigiano Reggiano over the tomatoes.

Fold the edges of the dough up over the filling, pleating as you go. Brush the egg wash over the crust, then sprinkle with 2 tablespoons of grated Parmigiano Reggiano.

Bake for 35-40 minutes, rotating the baking sheet halfway through, until the crust is golden brown and the tomatoes are slightly caramelized.

Let cool slightly, then garnish with fresh basil before serving.