In a large skillet over medium heat, add olive oil and saute the diced potatoes. Season the potatoes with garlic powder, onion powder, paprika, salt, and pepper for about 15 minutes.
While the potatoes are cooking, warm the tortillas on the stove-top or in the microwave.
In a small bowl, whisk together the eggs, along with a pinch of salt and pepper.
In a separate skillet, cook the chorizo for 7-8 minutes, breaking the chorizo up with a wooden spoon. Add the eggs to the chorizo and cook the eggs together with the chorizo for about 5 minutes until the eggs are cooked.
Pour your chorizo and egg mixture into the potatoes and add the shredded cheese. Mix it until the cheese melts completely.
Take about 1/4 cup of your egg and potato filling, and place it into a warm tortilla. Roll the tortilla up, ensuring the sides are tucked inward to prevent the filling from coming out of the sides. Repeat with the remaining tortillas.
Enjoy the burritos right away while still warm, or follow the directions below for freezing.