In a large bowl, combine bulgur and 1 cup boiling water. Cover tightly and let sit until bulgur is tender, 30 minutes. Strain through a fine-mesh sieve, pressing to remove liquid, then return bulgur to bowl. In a food processor, pulse pinto beans until coarsely chopped. Add beans to bulgur, along with Swiss cheese, carrots, scallion, and egg. Season with salt and pepper; mix well.
In a large skillet, heat olive oil over medium. Add 1/2 cup bean mixture and press lightly with a spatula to flatten. Make 3 more patties, working in batches if necessary (add more oil for second batch), and cook until browned and cooked through, 3 minutes per side. Serve burgers on buns with sprouts and avocado slices.