Prepare the dough by sifting the flour and mixing it with salt.
Incorporate the cold butter using a pastry blender, fork, or food processor until crumbly.
Add the ice water slowly and mix until well combined.
Wrap the dough in plastic wrap, form a disk, and chill in the refrigerator for at least 1 hour.
Heat the oil in a large skillet over medium-high heat and sauté the onion until soft.
Add the carrot, garlic, red pepper, and mushrooms. Stir in the soy sauce and cook until water evaporates.
Lower the heat, add basil, parsley, salt, and pepper. Let the filling cool.
Preheat the oven to 180°C and line a baking sheet with parchment paper. On a floured surface, roll out the dough to about 3mm thick.
Using a circular cutter, cut out 9cm diameter circles.
Place a spoonful of filling on half of each circle and add some cheese.
Moisten the edges of the circle with water and fold the dough into a semicircle, sealing the edges with a fork.
Arrange the empanadas on the baking sheet and brush the surface with a beaten egg.
Bake for 25-30 minutes or until golden. Let cool slightly before serving.