Mash the black beans with the back of a fork or a masher. (They can be slightly chunky.)
Add the minced vegetables to the beans, then mix in the seasonings to combine.
After seasoning to taste, add the beaten egg and combine. Stir in the bread crumbs and, if you’re using them, the cheese and corn. (At this step it may be easier to knead with clean hands.)
Form into 5 to 6 patties, depending on the amount of add-ins you’ve included.
If baking, place the patties on a cookie sheet that has been sprayed with non-stick cooking spray, and bake for approximately 10 minutes each side in a 375° oven. Flip once.
Alternatively, the patties can be cooked in a lightly oiled frying pan over medium heat — approximately 5 minutes each side. Flip once.
Serve on buns with the usual burger toppings.