Heat olive oil in a small skillet over medium heat. Add your onions, carrots, and peppers. Saute for 4-5 minutes, until softened. Add garlic and stir for 30 seconds. Add the ketchup, mustard, cumin, chili powder, and salt. Stir to combine.
Remove vegetables from heat and set aside to cool. Once they’re cool enough to handle, place the vegetables into a food processor with the black beans and bread crumbs and pulse a few times to combine.
Form the mixture into two large patties. Place them on a foil-lined baking sheet coated lightly with oil and bake for 15 minutes at 450°. The burgers will hold together, but they’ll always be slightly mushy and have a tendency to crumble if handled too much. Just place them on a bun using a spatula and garnish with your favorite burger toppings.