In a food processor, pulse the rinsed and drained black beans a few times until they are mostly mashed but still have some texture. Avoid over-processing into a paste.
Transfer the mashed beans to a medium bowl. Add the rolled oats, chopped red onion, chopped bell pepper, minced garlic, chili powder, cumin, smoked paprika, cayenne pepper (if using), and chopped cilantro. Mix everything together well.
Add the lightly beaten egg (or flax egg) and breadcrumbs to the bean mixture. Season with salt and pepper. Stir until just combined. The mixture should be firm enough to form patties. If it seems too wet, add a tablespoon more breadcrumbs at a time until it holds its shape.
Divide the mixture into 4 equal portions and form them into patties, about 3/4 inch thick. Press them gently to ensure they are compact.
Heat the olive oil in a large skillet over medium heat. Carefully place the black bean patties in the hot skillet, ensuring not to overcrowd the pan (cook in batches if necessary).
Cook for about 5-7 minutes per side, until golden brown and heated through. The edges should be slightly crispy.