Meanwhile, combine broth and half of pinto beans in bowl and mash with fork or potato masher. Heat oil in 12 inch nonstick skillet over medium heat until shimmering. Add onion and cook until just beginning to brown. Stir in tomato paste, garlic, cumin, oregano, and Chile powder and cook until fragrant, about a minute. Add beef, breaking up pieces with spoon, and cook until no longer pink.
Add swiss chard, and bean mixture. Cook, stirring constantly, until nearly all liquid has evaporated. Stir in remaining whole beans, lime juice, and salt. Remove from heat, cover and set aside.
Adjust oven rack 3 inches from broiler and heat broiler. Line rimmed baking sheet with foil. Wrap tortillas in clean dish towel and microwave until soft and pliable about 90 seconds. Arrange tortillas on counter. Dived rice, beef and bean filling and all but 1 cup of cheese among tortillas. Dollop each tortilla with 1 Tbsp of sour cream if desired. Fold sides of tortilla over filling and roll tightly into burrito form. Transfer to prepared sheet, seam side down.
Sprinkle remaining 1 cup cheese over burritos. Transfer to oven and broil until cheese is melted and starting to brown, about 3-5 minute, rotating sheet halfway through. Serve with additional sour cream and salsa