Preheat oven: Heat oven to 400°F (205°C). No need to grease the square tart pan — the dough fat will handle release.

Macerate the berries: Gently combine 170 grams fresh raspberries and 170 grams fresh blackberries with 0.3 cups granulated sugar, 1.5 tablespoons cornstarch, 1 tablespoons lemon juice, 0.5 teaspoons lemon zest, and 0.5 teaspoons vanilla extract. Toss carefully — you want the berries coated but not crushed. Let sit 10 minutes so the sugar draws out juice and the cornstarch hydrates.

Fit the dough: Unroll or unfold the round dough and lay it over the square tart pan. Gently press it into the corners and up the sides. The dough will not reach all four corners cleanly — that's expected. Let the overhang drape over the edges naturally. Do not trim anything yet.

Fill and dot with butter: Pour the berry mixture into the dough-lined pan, including any accumulated juices. Scatter 2 tablespoons unsalted butter, cold, cut into small pieces evenly over the top of the berries.

Fold the edges: Fold the overhanging dough up and over the outer edge of the filling, pleating as needed. The round dough in a square pan will create irregular, rustic folds — lean into it. The center will remain open.

Egg wash and sugar: Brush the folded crust edges with 1 egg, beaten (egg wash), then sprinkle with 1 tablespoons coarse or turbinado sugar (for crust). This gives the crust color and a light crunch.

Bake: Bake at 400°F for 35–40 minutes, until the crust is deep golden and the berry filling is bubbling across the full surface — not just at the edges. If the crust browns too fast, tent the edges loosely with foil for the last 10 minutes.

Cool completely: Let the tart cool in the pan on a wire rack for at least 45 minutes before slicing. The filling needs time to set or it will run. Dust with 1 tablespoons powdered sugar (optional, for finish) just before serving if desired.