Cook instant rice as directed on package. In a large pan on medium-high heat, add 1 tablespoons of the oil, the adobo sauce, bbq seasoning, smoked paprika, rotisserie chicken, corn, lime juice, and scallions. Sauté until everything is combined and coated, and the chicken is warmed through, 5-6 minutes.
Drain the baked beans over a bowl to reserve the liquid for the topping, set liquid aside. Add the beans to the chicken mixture, and then stir in the rice, and 1 cup of cheese, salt and pepper. Remove from heat.
Add about 1/2 cup of the filling to each tortilla. Fold one of the tortillas first by overlapping the line of the filling with the flap closest to you. Tuck in both sides and while holding them, fold the tortilla over itself, keeping the ingredients tucked tightly in the center. Fill and fold the remaining tortillas.
Preheat the oven to low broil.
Preheat a flat top griddle or large pan on med-high heat, add the remaining tablespoon of oil. Add each burrito seam-side down and sear until golden brown, 2-3 minutes. Flip and sear the other side, another 2-3 minutes. Transfer the burritos to an oven-safe baking dish.
Drizzle the reserved bean liquid over the burritos, top evenly with the shredded cheese, and place under the broiler until the cheese is just melted, 3-5 minutes. Serve with optional fixings like avocado, cilantro, sour cream, or hot sauce!
The filling makes a lot! You can fill as many burritos as you can, and then freeze the extras before the flat top grilling part.
The number of burritos you make will depend on how large your tortillas are.