How to Make It
Preheat the oven to 375°. Rub the sweet potato with 1/2 teaspoon of the olive oil and prick all over with a fork 5 or 6 times. Roast in a pie plate for about 1 hour, until tender. Let cool slightly. Halve the sweet potato lengthwise and scrape the flesh into a large bowl. Mash with a fork.
In a food processor, pulse the kidney beans until coarsely chopped. Transfer to the bowl with the sweet potato.
In a medium skillet, heat 1 tablespoon of the olive oil until shimmering. Add the shallots, garlic, and jalapeño and season with generous pinches of salt and pepper. Cook over moderate heat until softened, about 3 minutes. Scrape the vegetables into the bowl with the sweet potato and, using a rubber spatula, mix until just combined. Add the cheese, the 3 tablespoons of mayonnaise, the cilantro, cumin, coriander and paprika and mix until combined. Season with salt and pepper.
Line a rimmed baking sheet with parchment paper. Press heaping 1/2-cup portions of the burger mixture into 6 patties. Transfer to the prepared baking sheet. Refrigerate for 30 minutes, until the patties are slightly firm.
Sprinkle the cornmeal in a pie plate. Working one at a time, carefully dredge each patty in the cornmeal, pressing gently to help the cornmeal adhere. Place the patties back on the baking sheet.
In an extra-large nonstick skillet, heat 1 1/2 tablespoons of the olive oil until shimmering. Add 3 of the patties to the skillet. Cook over moderate heat, flipping once, until browned on both sides and hot through, about 6 minutes. Transfer to a platter. Repeat with the remaining patties and oil.
Transfer the burgers to the buns, top with tomatoes, lettuce and onion, and serve.