Prepare grill for direct cooking over medium-high heat, about 450 degrees F.
Place tomatillos and jalapeno on grill grate and cook, with the lid closed, turning them occasionally, until jalapeno skin is blackened and blistered (about 5 minutes) and tomatillos are browned but not bursting (7 to 9 minutes). Transfer them to a bowl as they are done, and let cool.
Scrape and discard skin from jalapeno. Seed jalapeno, reserving seeds.
Pulse avocado, tomatillos and any juices, jalapeno (without seeds), onion, cilantro, oil, garlic, salt and sugar in a blender or food processor until smooth.
For a spicier salsa, add seeds. Transfer to a medium saucepan and bring to a simmer over medium heat. Reduce heat to very low to keep salsa warm. Extra salsa can be stored in the refrigerator and kept up to 3 days.
Lightly oil grill grate. Brush pork with oil and season with chili powder and salt. Grill pork over medium-high heat, with lid closed, about 4 minutes per side, or until the internal temperature reaches between 145 degrees F. (medium rare) to 160 degrees F. (medium) on a digital meat thermometer. Remove from grill and let rest for 3 minutes.
Place tortillas on grill grate and cook until heated, about 30 seconds per side. Remove from grill and wrap in a napkin to keep warm.
To assemble burrito:
Chop pork into bite-sized pieces.
For each burrito, spread 2 tablespoons of beans in a wide strip on center of tortilla. Top with rice and cheese, evenly distributed between the burritos, and 1/6 of chopped pork.
Sprinkle with cilantro. Fold in right and left sides, and roll up tortilla from the bottom. Transfer each to a dinner plate. Smother each with one sixth of warm salsa, add lime wedges and serve immediately.