For the black bean burger:

1. Set aside 1/2 cup black beans.
2. In a food processor, pulse remaining black beans, mushrooms, shallots, jalapeño peppers, barbecue sauce, tabasco chipotle pepper sauce, ancho or chile powder, and cumin until a chunky purée forms.
3. Transfer purée to a medium bowl and mix in oats, rice, egg white, and reserved beans; season with salt and pepper.
4. Form mixture into patties about 1/2-inch thick; cover and chill for 1 hour.
5. Heat a pan to medium-high; add a touch of olive oil and sear patties on both sides until crisp.

For the rajas:

1. Preheat oven to 450°F, or heat a broiler or charcoal grill to medium-high, or gas grill to high.
2. For the oven or broiler, mix peppers, oil, salt, and pepper in a large bowl; place on a rimmed baking sheet. For a grill, oil grill grate and place peppers directly atop.
3. Roast 15 to 20 minutes, turning occasionally, until tender and charred. Transfer to a large bowl, cover with plastic wrap, and let steam for 15 minutes. Peel peppers and slice in half; discard seeds and slice crosswise into 1/4-inch strips.

For the corn relish:

1. In a bowl, combine all ingredients and season with black pepper.

To assemble:

1. Toast buns on the grill or oven. Place patty on bun and top with cheese, roasted rajas, and corn relish. Serve with extra barbecue sauce.