Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.

In a skillet over medium heat, cook the chorizo, breaking it up with a spoon, until browned (about 5-7 minutes). Remove chorizo with a slotted spoon, leaving the rendered fat in the pan.

Add the diced potatoes to the skillet with the chorizo fat. Cook for 8-10 minutes until tender and slightly crispy. Season lightly with salt.

Lower the heat, add the beaten eggs to the potatoes, and scramble gently until just set but still moist. Stir in the cooked chorizo and green onions, then remove from heat to cool slightly.

Once the mixture is warm (not hot), stir in the shredded cheese.

Place about 2 tablespoons of filling into the center of each empanada disc.

Fold the dough over the filling to create a half-moon shape. Crimp the edges firmly with a fork to seal tight.

Whisk the remaining egg with 1 tablespoon of water to make a wash and brush it over the tops of the empanadas.

Bake for 20-25 minutes, or until the pastry is golden brown and flaky. Let cool for 5 minutes before serving.