Peel the potatoes, wash them, and cut them into 1/4″ (1/2 cm) thick slices. Peel the garlic cloves and finely chop them.
Heat the oil in a large skillet and sauté the potatoes until they are golden brown.
Add the garlic, chorizo, and parsley.
Mix well for 3 minutes, then remove from heat and drain in a colander.
Beat the eggs with salt, Espelette pepper, cumin, and oregano.
Add the potatoes and chorizo mixture to the eggs and mix well.
Preheat the oven to 400 F (200 C).
Pour the mixture into a buttered 8″ (20 cm) square dish.
Bake for 25 to 30 minutes, or until the frittata is set.
Serve warm or at room temperature, cut into cubes.