Heat a large (approximately 10 inches wide), non-stick skillet over medium heat on the stove. Use a skillet that is oven-safe. Add the oil to the skillet to heat.
When the oil is hot, add the sausage. Continue to cook, breaking up the meat, until it is cooked through completely and resembles ground beef, approximately 5 minutes.
While the sausage is cooking prepare the egg mixture. In a medium bowl, whisk together the eggs, salt, and pepper until well blended.
When the sausage is cooked, add the egg mixture, green chiles, and cotija cheese to the skillet. Stir to combine. Using a rubber spatula, run the spatula around the edges of the egg mixture, lifting it up to get the raw egg on the bottom. Do not mix as you will get scrambled eggs.
Continue cooking until the bottom of the eggs are set and the edges are starting to set, approximately 5 minutes. It should look about half way cooked overall.
Place the skillet in the oven and continue cooking until the eggs are cooked through and it is dry to the touch on top, approximately 6-8 minutes. Serve warm.
Notes
The smaller the skillet, the thicker your frittata will be and the longer it will need to cook. The larger the skillet, the thinner the frittata and the faster it cooks.A non-stick skillet is best, but you can also use a cast iron skillet. The egg tends to stick more in cast iron, making it difficult to flip out if you choose to do so.Top with your favorite condiments like avocado, salsa, cilantro, or more cheese!