In a large mixing bowl, combine the cooked rice, black beans, corn, sliced red onion, and sliced jalapeño. Season the mixture generously with salt, pepper, and half of the chopped cilantro. Stir thoroughly until all ingredients are well integrated.
On a clean surface, lay out the flour tortillas. Evenly distribute the rice and bean mixture onto each tortilla. Top each with an equal portion of shredded Monterey Jack and cheddar cheese. Gently place avocado slices and add a spoonful of chipotle sauce over the filling for flavor enhancement.
Carefully fold in the sides of each tortilla to encase the filling. Then, starting from the bottom, roll the tortilla tightly upwards, ensuring the filling remains secure and contained.
Preheat a skillet or grill pan over medium heat and drizzle a small amount of olive oil to coat the bottom. Place the filled tortillas seam side down in the heated pan. Grill for approximately 3-4 minutes until the bottom is golden brown and crispy. Carefully flip and grill the other side for another 3-4 minutes until similarly golden.
Once the melts are golden and the cheese has melted to perfection, remove them from the heat. Cut each wrap in half diagonally for an appealing presentation. Serve hot, garnished with the remaining chopped cilantro and a mound of shredded lettuce. Additionally, provide extra chipotle sauce or your preferred salsa on the side for dipping.