Either line a baking sheet with parchment paper or have a 9- to 10-inch (23cm) tart mold or dish ready, one that doesn't have a removable bottom. (If yours does have a removable bottom, I advise baking the tart on a parchment lined baking sheet in case of any drips.) Preheat the oven to 425ºF (220ºC).
On a lightly floured surface, roll the dough into a 13-inch (33cm) round. If it cracks around the edges when you start to roll it, pick up the dough, hold it perpendicular to the counter, and gently pound the edges on the counter as you turn it, to make the edges more malleable. Then continue to roll the dough into a circle. Transfer the dough into the baking dish or onto the baking sheet.
Mix the blackberries, cherries, brown sugar, flour, vanilla, crème de cassis or orange liqueur (if using), lemon zest and juice in a bowl.
Distribute the berry filling over the dough, leaving a couple of inches (~5cm) of space around it (if using a baking sheet), which you can now fold the dough over the berries to create the crust. Brush the top edges of the dough with melted butter and sprinkle with large-grain or granulated sugar.
Bake for 25 minutes, or until the berries are cooked through and bubbling, and the dough is nicely browned. Let the tart cool for a few minutes if it's on a sheet pan, then slide the tart onto a cooling rack, which is easier if using a flat baking sheet. (A rimmed one might require a bit of finesse, but I do it all the time and I know you can do it too.) If using a baking dish and it's sticking and not coming out easily, you can let it cool in the pan. Mine is non-stick so comes out easily.