Mix flour and salt in a large bowl. Add the shortening and cold coconut oil over the flour and start cutting the fats with knifes, mixing with the flour, until obtaining a sand-like consistency.
Mix the tofu, vinegar, and water, then add to the flour bowl. Using a spatula, keep mixing the ingredients until a compact ball is formed. Refrigerate for at least 30 minutes, ideally 2 hours.
Put the tomatoes in halves, garlic, and salt in a bowl and allow to set for around 15 minutes. Remove their liquid and mix in the peeled physalis.
Put almonds, lemon, and half a teaspoon of salt in a blender and blend until obtaining a paste.
Preheat the oven to 430°F.
Roll out the dough over plastic wrap and cover with it. Extend with a rolling pin from the center, pushing to the edges, making a circle about 14.5 inches in diameter.
Remove the top plastic wrap, and slightly rolling the dough over the rolling pin, transfer it to the baking tray. Remove the rest of the plastic and scatter the almond mixture over the dough, then the cheese, and finally the tomato mixture, leaving about 2 inches free around the edge. Fold carefully until completely closed.
Bake for about 20 minutes or until the dough is brown.
