Preheat your oven to 375°F (190°C).
In a large mixing bowl, combine the gluten-free all-purpose flour, almond flour, granulated sugar, and salt. Add the cold butter cubes and use a pastry cutter or your fingers to work the butter into the flour mixture until it resembles coarse crumbs.
In a small bowl, whisk together the egg and vanilla extract. Add the egg mixture to the flour mixture and stir until a dough forms. If the dough seems too dry, you can add a tablespoon of cold water.
Transfer the dough onto a lightly floured surface and knead it a few times to bring it together. Roll out the dough into a circle large enough to fit your tart pan.
Grease a tart pan with a removable bottom and carefully transfer the rolled-out dough into the pan. Press it into the bottom and sides of the pan, trimming any excess dough.
In another bowl, combine the mixed fresh berries, granulated sugar, cornstarch, lemon juice, and lemon zest. Gently toss until the berries are coated evenly.
Pour the berry filling into the prepared crust, spreading it out evenly.
Place the tart pan on a baking sheet to catch any drips and bake in the preheated oven for 40-45 minutes, or until the crust is golden brown and the filling is bubbling.
While the tart is baking, prepare the glaze. In a small saucepan, heat the berry jam or jelly with the water over low heat until it becomes smooth and pourable.
Remove the tart from the oven and let it cool for a few minutes. Brush the glaze over the top of the tart, coating the berries with a thin layer.
Allow the tart to cool completely before slicing and serving. You can refrigerate it for a couple of hours if you prefer it chilled.