In a skillet over medium heat, cook the chorizo until browned and cooked through. If using raw chorizo, break it up with a spatula as it cooks. Once done, remove the chorizo from the skillet and set it aside.
In a mixing bowl, whisk together the eggs and season with salt and pepper. In the same skillet, add a bit of butter or olive oil, then pour in the eggs. Scramble the eggs over medium heat until they are fluffy and fully cooked, about 3-5 minutes.
While the eggs are cooking, warm the flour tortillas in a separate pan or microwave until soft and pliable.
To assemble the burritos, place a portion of the egg mixture in the center of each tortilla, followed by the cooked chorizo and a generous sprinkle of shredded cheese. Add any optional toppings you desire.
Carefully fold in the sides of the tortilla and then roll it tightly from the bottom to enclose the filling. Repeat with the remaining tortillas.