Add the pepper, onion and garlic cloves to the bowl of a food processor fitted with a metal blade.
Put the lid in place and pulse, stopping to remove the lid and scrape down the sides of the bowl, until the ingredients are finely chopped.
Add half of the black beans, all of the seasonings, salt and tomato sauce to the food processor and pulse, scraping down the sides of the bowl as necessary, until the mixture resembles the consistency of guacamole (slightly chunky but a cohesive paste.)
Scrape the bean and vegetable mixture into a mixing bowl and stir in the remaining beans and corn, then the egg and breadcrumbs.
Test the consistency of the mixture. You should be able to roll the mixture into a ball and flatten into a patty without it sticking to your hands. If you cannot, add one extra tablespoon of breadcrumbs at a time, stirring and checking the consistency after each addition until it does what it should. The goal is to add enough that the mixture ceases to be sticky but not so much that it becomes crumbly. I found that in each of the batches I made, I needed significantly different amounts of breadcrumbs to hold the patties together, but I never needed less than 1 cup.
Roll balls of the bean mixture according to the size of the burger you'd like: golf ball size for sliders, peach size for standard burgers, navel orange size for mega-burgers.
Place a heavy-bottomed skillet over medium-high heat and pour in enough oil to cover the bottom by about 1/8-inch. When the oil is shimmering, flatten each ball into a patty that is about 1/2 to 3/4-inch thick and slide it into the oil. Do this with as many patties as you can comfortably fit into the pan without crowding. Fry for about 3-4 minutes on each side, or until deep brown and crunchy on the outside.
Transfer the patties to a paper towel lined platter.