Reserve 1/2 cup beans. Pulse remaining black beans, mushrooms, onion, green chiles, hot sauce, chili powder and cumin a few times in a food processor until mixture resembles a chunky puree. Place mixture in a medium bowl. Add brown rice, panko crumbs, egg, salt and pepper and mix until well combined. Form into 5-6 patties, depending on how big you like your burgers. Cover and place in refrigerator for one hour or up to overnight.
Chipotle Mayo: Combine all ingredients in a blender or small food processor. Puree until smooth. Season, to taste, with salt and pepper. Place in an airtight container in refrigerator until ready to use.
Place olive oil in a large nonstick skillet over medium-high heat. Cook burgers, for about 10 minutes, turning once, until heated through. Top with a slice of cheese and cook until melted.
Place burger on top of a few slices of lettuce. Top with some chipotle mayo, tomato slices, and a few more pieces of lettuce to make a bun.