Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper for the burgers. Place the ears of corn on a separate baking sheet.
Brush the corn with melted butter or olive oil. Season with salt and pepper. Stick the corn in the oven and roast for 15 to 20 minutes. Slice it off the cob once finished. You can also grill the corn if you wish. You can also just use regular corn - whether it’s sliced fresh from the cob or cooked in a steamfresh bag. Reduce the oven heat to 350 degrees F when the corn is done.
While the corn is roasting, heat a skillet over medium-low heat and add the olive oil. Add the shallot, pepper, garlic, a pinch of salt and pepper and cook until softened, about 5 minutes. Turn off the heat.
Place three quarters of the black beans in a large bowl and mash them with a fork or a potato masher. Add the rest of the black beans, the corn, the shallot/pepper mixture, the bread crumbs, paprika and cumin. Stir to combine. Stir in the BBQ sauce, worcestershire sauce and eggs. Form the mixture into patties. Place each patty on the parchment paper. If desired, you can give each a little spritz of olive oil so the tops crisp up.
Bake for 12 minutes. Gently flip (use a spatula and your hand to flip!) and bake for 12 to 15 minutes more. A minute or so before they are done, top with cheddar and let it melt in the oven. Serve immediately on buns with pickled onions and your favorite spread.