1. Heat a 12-inch nonstick skillet over medium high heat. Brown chorizo, 2 to 3 minutes, then remove from pan. Add oil, garlic, then shrimp. Season shrimp with salt and pepper and cook shrimp until pink, 2 or 3 minutes. Transfer shrimp to a cutting board and coarsely chop.
2. Add a drizzle of oil to the pan and a large tortilla. Cook tortilla 30 seconds, then turn. Sprinkle cheese over half the tortilla. Then top with chorizo and shrimp. Fold tortilla over. Cook folded tortilla slightly to melt cheese and crisp. Remove quesadilla to large cutting board and repeat with remaining ingredients. Cut each quesadilla into wedges and enjoy with preferred sides.