Pulse the oats in a food processor fitted with the 'S' blade 5 times to roughly chop the oats. Add one can of black beans and pulse an additional 5 times to create a chunky paste.
Add the egg, cumin, coriander, and salt to the food processor. Process until most of the large pieces are gone. You will be left with a thick paste that will act like the "glue" for the black bean burger.
In a medium-sized bowl, mix the remaining can of drained and rinsed black beans with the cooked wild rice or wild rice blend, cilantro, garlic, jalapeno, green onion, and cheese. Stir to combine. Add the mixture from the food processor, season with salt then stir again until all of the ingredients are completely combined.
Line a baking sheet with parchment paper and wipe on a bit of whatever oil you will be cooking with. Measure out 1/2-cupfuls of the veggie burger mixture then form into 6 patties. Chill for at least 30 minutes.
Heat a cast-iron or heavy-bottomed skillet over medium-high heat. See note if using a glass cooktop. Once the pan is hot, add 1 tablespoon of oil and place the desired amount of black bean patties in the pan being careful to not overcrowd the pan. You may have to cook the patties in batches if cooking all 6 at once.
Cook the burgers until a golden brown crispy crust has formed, about 3-4 minutes, flip and cook 4-5 minutes more.