Drizzle olive oil on a skillet. Sauté the chorizo over medium to high heat until it turns brown and crumbles.
Add onion, oregano, paprika, chili pepper to the pan. Cook, stirring occasionally until the onion softens.
Whisk eggs in medium bowl, and then pour them into the chorizo mixture. Add salt and reduce heat to medium-low. Continue to stir and cook until the eggs are scrambled and no longer liquid.
Heat flour tortilla in the microwave for 30 seconds. Scoop chorizo-egg mixture into the center of the tortilla and cover it with shredded Cheddar cheese. Roll it up like a burrito.