In a small bowl, combine the flaxseed meal and 3 tablespoons of water. Stir well and let sit for 5 minutes until it forms a thick, gel-like 'flax egg'. This acts as your binder.
In a large mixing bowl, add the drained and rinsed black beans. Use a potato masher or a sturdy fork to mash the beans until mostly smooth, leaving some small chunks for texture.
Add the cooked brown rice, Panko breadcrumbs, smoked paprika, garlic powder (if using), onion powder (if using), salt, black pepper, and the prepared flax egg to the mashed beans. Mix thoroughly with your hands until all ingredients are well combined and the mixture is sticky enough to form patties.
Divide the mixture into 4 equal portions and form them into burger patties, about 3/4-inch thick. If the mixture is too wet, add a tablespoon more breadcrumbs; if too dry, add a teaspoon of water until desired consistency is reached.
Heat olive oil in a large skillet over medium heat. Carefully place the patties in the hot skillet (you may need to cook in batches). Cook for 6-8 minutes per side, or until deeply golden brown and heated through. Alternatively, grill the patties over medium heat for 6-8 minutes per side.
Serve immediately on your favorite burger buns with desired toppings like lettuce, tomato, onion, pickles, and vegan mayonnaise or ketchup.
Notes
Storage: Leftover patties can be stored in an airtight container in the refrigerator for up to 3-4 days. Reheat gently in a skillet or oven. You can also freeze uncooked patties for up to 2 months; thaw before cooking.Variations: Feel free to customize the spices! Add a pinch of cayenne for heat, a dash of cumin for an earthy flavor, or a tablespoon of nutritional yeast for a cheesy note.