Prepare Ingredients.
Stir together mayonnaise, lime juice, hot sauce, and old bay seasoning in a small bowl. Refrigerate until serving.
Blot shrimp dry with paper towels and add to a bowl. Add old bay seasoning and cumin. Stir to coat shrimp.
Heat avocado oil in a skillet over medium heat for 2 minutes. Add shrimp to hot skillet and cook for 5 minutes or until shrimp is fully cooked, stirring regularly. Divide brown rice, black beans, red onion, lettuce, shrimp and cheese in the center of 2 tortillas. Fold and roll tortillas to secure.
Heat a large skillet over medium heat and grease with cooking oil. Place burritos on skillet seam side down and cook for 1-2 minutes. Flip and cook 1 minute longer.
Slice burritos in half and serve warm with spicy mayonnaise for dipping.
