Rustic Berry Tart

for the crust: 1 1/2 cups all-purpose flour 2 tsp granulated sugar 1/2 tsp salt 5 1/2 oz. unsalted butter (cold) 1 large egg yolk 3 tbsp whole milk for the berries: 4 cups fresh berries (i prefer to go heavy on the blackberries,) rinsed and picked over 1/4 cup granulated sugar, more to taste 1 tbsp flour 1 tsp finely grated lemon zest pinch of salt to finish: 1 large egg, beaten granulated sugar Combine the flour, sugar, and salt in a stand mixer with the paddle attachment. cut the butter into 1/2 inch cubes and add them to the flour mixture. On low speed, mix for two minutes, if afterwards there are lumps larger than peas, break them up with our fingers. In a small bowl mix the yolk with the milk and add them to the flour mixture. Mix on low for about 20 seconds to form a dough. Turn out the dough onto plastic wrap, form into a disk, wrap and refrigerate for at least 20 minutes, or up to two days. ( Before rolling it out, let sit at room temperature for 10 min) Line a rimmed baking sheet with parchment paper. On a floured surface, roll out the dough to a 13 inch round, allowing the edges to be a bit rough. Transfer the round to the baking sheet. Toss the berries with sugar, flour, lemon zest, and salt. Heat oven to 350F. Heap the berries in the center of the dough. Using your fingertips, fold the edges of the dough over the fruit to form a rim about two inches wide. Pleat the dough as you go. Brush the dough with the beaten egg, and sprinkle with additional sugar. Bake until the crust is a deep golden brown, check after 1/2 hour.