Prepare the flax egg. In a small bowl, mix together the ground flaxseed meal and water. Let it sit for about 5 minutes to thicken and form a gel-like consistency. This will act as a binder for the burger patties.
In a large mixing bowl, add the drained and rinsed black beans. Use a fork or potato masher to mash the beans until they are mostly broken down but still have some texture.
Combine the ingredients. Add the rolled oats, chopped onion, minced garlic, prepared flax egg, soy sauce or tamari, smoked paprika, ground cumin, chili powder (if using), salt, and pepper to the mashed black beans. Mix everything together until well combined. The mixture should be sticky and hold together easily.
Divide the mixture into equal portions and shape them into burger patties of your desired size and thickness. If the mixture is too wet, you can add a little more oats to help bind it together.
Heat 1-2 tablespoons of olive oil in a large skillet over medium heat. Once hot, add the burger patties to the skillet, making sure not to overcrowd them. Cook for 4-5 minutes on each side, or until golden brown and crispy.
Once the patties are cooked through and crispy on the outside, remove them from the skillet and let them cool slightly before serving.
Serve these vegan oat and black bean burger patties on burger buns with your favorite toppings and condiments, such as lettuce, tomato, avocado, onions, pickles, mustard, or vegan mayo.