Remove the chorizo from the casings and saute in a large skillet over medium heat until cooked through. Drain the excess grease from the skillet.
While the chorizo is cooking, remove the kale leaves from the stems and tear into small pieces. Place in a colander and rinse well. Once the chorizo is fully cooked and drained, add the kale to the skillet. Cook until the kale is fully wilted.
Begin to preheat the oven to 350 degrees. In a bowl, whisk the four eggs until they are fairly smooth. Next, whisk the milk and parmesan into the eggs. If you will be baking the frittata in the cast iron skillet, pour the egg mixture directly over the cooked chorizo and kale. If you are cooking the frittata in a casserole dish, spray it lightly with non-stick spray, add the cooked chorizo and kale to the bottom, and then pour the egg mixture over top.
Sprinkle the shredded mozzarella over the top of the frittata. Place in the preheated oven and bake for about 45 minutes or until the frittata looks puffy and golden brown on top. Slice into six pieces and serve hot.