Using a fork, mash the beans in a medium bowl until they are mushy but still have some whole bean pieces throughout.
Make the burger mixture.
Mix the breadcrumbs, grated onion, chili powder, egg and some salt and pepper into the beans. Add a splash of water if the mixture looks dry. Set aside for 5 minutes. Preheat a large cast-iron skillet over medium-high heat and add a few tablespoons of canola oil.
Form the patties.
Divide the bean mixture into 4 equal balls and form into 4 nice, neat patties. Black bean burgers don't shrink when they cook, so whatever size you make them when they go into the skillet will be the size they are when they come out.
Cook the burgers.
Cook the burgers until browned, 4 to 5 minutes on each side. Add a slice of Swiss cheese to the top of each burger. Invert a second skillet on top of the first skillet and continue cooking, 2 minutes, until the cheese is melted.
Top the burgers.
Combine the mayonnaise and some hot sauce in a small bowl. Serve the burgers on toasted buns with the spicy mayonnaise, lettuce and sliced tomatoes.