In a food processor, combine 1.5 cups of all-purpose flour, 0.5 teaspoons of salt, and 0.5 teaspoons of garlic powder. Add 0.5 cup of cold diced butter and pulse until it resembles coarse crumbs. Gradually drizzle in 4 tablespoons of ice water and 3 teaspoons of olive oil, pulsing until a soft dough forms. Shape into a disc, wrap in plastic, and chill in the refrigerator for 30 minutes.

After the dough has chilled, preheat your oven to 375°F (190°C). On a floured surface, roll out the chilled crust into a 14-inch circle. Carefully transfer the dough to a parchment-lined baking sheet to prevent sticking. Return the rolled dough to the fridge while you prepare the filling to keep it firm and workable.

In a mixing bowl, combine 1 cup of fine dry bread crumbs, 0.25 cup of melted butter, 2 tablespoons of shredded Parmesan cheese, and 0.5 teaspoons each of ground thyme, garlic powder, and salt. Mix well to create a flavorful base. Spread this mixture evenly across the prepared crust, leaving about a 2-inch border for folding.

Layer your sliced heirloom tomatoes, halved cherry tomatoes, and torn basil leaves in the center over the breadcrumb mixture. Strategically place sliced mozzarella balls around the filling to ensure each bite is delicious. Once the filling is arranged, gently fold the edges of the crust over the filling, creating a rustic look that leaves the center exposed.

For a glossy finish, brush the crust with an egg wash made from 1 beaten egg. Bake the Rustic Caprese Galette in your preheated oven for approximately 30 minutes, or until the crust is golden brown and crisp. Keep an eye on the galette as it bakes, ensuring it doesn't overbrown.

Once baked, remove the galette from the oven and allow it to cool slightly on the baking sheet. Before serving, drizzle with olive oil and garnish with remaining mozzarella and a fresh basil leaf for a touch of color and flavor. This Rustic Caprese Galette is now ready to impress your guests!