Heat oil in a non-stick skillet over medium-low heat. Add onion and cook for 2-3 minutes, until onions start to brown. Add chorizo chunks and bell pepper. Cook over low heat for 8-10 minutes.
In a small bowl, beat eggs well. Add to chorizo and onions. Cook for 2-3 minutes until eggs start to set. Turn the mixture over and break up with a spatula. Cook for 3-4 minutes until eggs have cooked through.
While the eggs cook, warm up a fresh dry skillet to medium-low heat. Heat the tortillas individually, 30 seconds per side. Ensure the tortilla stays soft and doesn't turn crispy.
Serve the cooked chorizo and egg filling into one half of each tortilla. Top with shredded cheddar cheese, sliced avocado, and salsa.
Fold the burrito by bringing up the edges around the filling, and use the edge closest to you to roll the burrito into a tight cylinder, making sure you don't tear the tortilla.
Cut in half to serve immediately, or roll in foil to take away.