In a large mixing bowl, whisk together the flour and salt. Add the cubed butter and use a pastry cutter or your fingers to work the butter into the flour until the mixture resembles coarse crumbs.
Gradually add the cold water, mixing until a dough forms. Shape the dough into a ball, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
On a lightly floured surface, roll out the chilled dough to about ⅛ inch thickness. Use a round cutter or a small plate to cut out circles of dough, approximately 4-5 inches in diameter.
Place some tomatoes, some diced mozzarella, and a teaspoon of pesto in the center of each dough circle. Season with salt and pepper. Fold the dough over the filling to create a half-moon shape. Use a fork to crimp the edges firmly to seal the empanadas. Trim any excess dough if necessary.
Transfer the sealed empanadas to the prepared baking sheet. Brush the tops with egg wash for a golden finish. Bake in the preheated oven for 20-25 minutes, or until the empanadas are golden brown and crisp.
Remove the Caprese Empanadas from the oven and let them cool slightly before serving. Drizzle with balsamic glaze and garnish with fresh basil leaves if desired. Enjoy these delicious empanadas warm as an appetizer, snack, or light meal.