Prepare the crust first. Cut the butter into small cubes and place into the freezer for at least 10 minutes. Place the cold butter, flour and salt into a food processor and pulse for about a minute, until the texture resembles fine crumbs. Add the cold water and pulse again for about 30 seconds until a dough ball forms. Remove the dough from the food processor and roll out on a lightly floured surface. The dough should be about 1/8th-inch thick and be 1 inch bigger than your tart pan. This recipe will work well with a 9-inch or 10-inch tart tin.
Gently transfer the rolled dough into the tart tin and press gently into the bottom and sides. Discard any extra dough. Pierce the dough all over with a fork, then place into the freezer to chill while preparing the filling.
Making the Frangipane:
Preheat the oven to 375F and prepare the filling. Place the softened butter, sugar and vanilla into a large mixing bowl and beat for 3 to 4 minutes, until the butter is light and fluffy. Begin adding the eggs, one at a time, and mixing well after each addition. The mixture should be smooth and creamy. Add the almond flour and all-purpose flour next and mix just until incorporated, about 30 seconds.
In a separate bowl, toss the berries in the cornstarch until they're well coated. Add the berries and lemon zest into the filling and fold gently. Remove the tart crust from the freezer and transfer the filling into the crust, spreading evenly. Bake in the preheated oven for 45 minutes, or until a toothpick inserted into the center comes out clean. Allow the tart to cool on a wire rack for at least 30 minutes before serving.
Note: after 45 minutes of baking, the tart will have a custard-like texture in the center. If you prefer a more well-done center, loosely tent the tart with foil after 45 minutes and continue baking for an additional 15 to 20 minutes. See my blog post above for blind-baking instructions, if you want to blind-bake the crust first.