First, make the burrito filling. Heat avocado oil in a large sauté pan over medium heat. Add diced onion and jalapeno and cook until softened, about 3 to 4 minutes.
Next, add pulled carnitas to the pan and cook for another 3 to 4 minutes, stirring occasionally, until carnitas are lightly crisped and warmed through.
Stir in the rice and beans, then add lime juice and a splash of the reduced carnitas juices (about 1 tablespoon). Stir to combine and cook for another 2 to 3 minutes until warmed through.
Finally, lower heat and stir in the shredded cheese until melted. Then remove from heat and set aside.
Next, warm the tortillas in the microwave between two dampened sheets of paper towels, for about 15 seconds per tortilla. Then transfer tortillas to a plate for wrapping the burritos.
Assemble the burritos. Spoon about a quarter of the filling into the center of each tortilla and shape it into a log. Fold opposite sides of the tortilla in towards the center (on the short sides of the filling "log"), then roll the burrito in the other direction to close, tucking the far side in with your pinky fingers.
Plate the burritos seam side-down and top with a generous helping of spicy verde sauce. Garnish with queso fresco and serve hot with a side of rice and beans, or chips, salsa, and guacamole!