Preheat the oven. Set to 400°F (200°C).
Lightly coat your 9x13-inch baking dish with cooking spray.
Season the shrimp. In a bowl, combine shrimp, olive oil, lime juice, garlic, chili powder, cumin, smoked paprika, oregano, salt, and pepper. Toss to coat. Let it sit while you prep the filling.
Make the filling base. In a large bowl, mix cooked rice, black beans, corn, bell peppers, red onion, and half of the cheese.
Stir in the salsa and Greek yogurt until everything is evenly coated. Taste and adjust salt as needed.
Quick-cook the shrimp. Heat a large skillet over medium-high. Add the seasoned shrimp in a single layer and cook 1–2 minutes per side, just until pink and opaque.
Do not overcook. Transfer to a cutting board and roughly chop into bite-size pieces.
Combine shrimp with filling. Fold the chopped shrimp into the rice-and-bean mixture. The heat from the shrimp will loosen the mixture slightly, which is perfect for rolling.
Assemble the burritos. Warm tortillas in the microwave for 20–30 seconds to make them pliable.
Place about 3/4 cup of filling on each tortilla, tuck in the sides, and roll tightly. Arrange seam-side down in the prepared baking dish.
Top and bake. Spread a few spoonfuls of extra salsa on top if you like a saucier bake. Sprinkle the remaining cheese evenly over the burritos.
Bake for 12–15 minutes, until the cheese is melted and the edges are lightly crisp.
Finish and serve. Garnish with chopped cilantro and green onions. Serve with lime wedges, extra salsa, and a dollop of Greek yogurt or guacamole if you’d like.