1. Preheat your oven to 350°F (175°C).
2. In a mixing bowl, combine flour and cold vegan butter. Use your fingers to mix until it resembles coarse crumbs.
3. Add cold water, one tablespoon at a time, until the dough comes together. Form into a disk, wrap in plastic, and refrigerate for 15 minutes.
4. Roll out the dough on a floured surface and fit it into a tart pan. Prick the bottom with a fork.
5. In another bowl, mix almond flour, sugar, softened vegan butter, all-purpose flour, almond milk, and vanilla extract until smooth.
6. Spread the frangipane filling evenly over the pastry crust.
7. Bake for 25 minutes or until the filling is set and the crust is golden brown.
8. Let it cool before serving.