Spread the rinsed beans over a clean kitchen towel or several layers of paper towels. Pat them thoroughly dry. The beans should feel slightly tacky rather than wet, with no visible water collecting around them.

Heat 1 tablespoon olive oil in a 12-inch skillet over medium heat. Add the onion and bell pepper. Cook for 5 to 6 minutes, stirring occasionally, until softened and most of their moisture has evaporated.

Stir in the minced garlic and cook for 30 seconds, just until fragrant. Transfer the vegetables to a large mixing bowl and allow them to cool for about 5 minutes. Wipe out the skillet.

Add the dried black beans to the bowl with the vegetables. Use a potato masher or sturdy fork to mash approximately two-thirds of the beans. Leave some beans whole or in large pieces for texture. The mixture should look chunky rather than smooth like a purée.

Add the oats, panko, beaten egg, soy sauce, lime juice, cumin, smoked paprika, chili powder, salt, and black pepper. Fold until evenly combined. The mixture should feel moist but hold together when firmly pressed.

Squeeze a small amount of the mixture in your hand. If it crumbles, stir in 1 tablespoon water. If it feels wet or sticky enough to slump, add 1 tablespoon additional panko and let it stand for 5 minutes.

Divide the mixture into 6 equal portions, about 2/3 cup each. Shape each portion into a patty approximately 3 1/2 inches wide and 3/4 inch thick. Press the edges firmly to close visible cracks.

Arrange the patties on a parchment-lined plate or small baking sheet. Refrigerate uncovered for 20 minutes. They should feel firmer and lift easily from the parchment after chilling.

Heat 1 tablespoon olive oil in the wiped skillet over medium heat. Add 3 patties, leaving space between them. Cook without moving for 4 to 5 minutes, until the bottoms develop a dark golden crust.

Turn the patties carefully with a wide spatula: Cook for another 4 to 5 minutes, until browned on the second side, firm through the center, and heated to 160°F (71°C). Transfer them to a plate.

Add the remaining 1 tablespoon olive oil to the skillet and cook the final 3 patties in the same manner. Reduce the heat slightly if the skillet begins to smoke or the crust darkens before the centers are hot.

Spread the toasted buns with mayonnaise or burger sauce, if using. Add the lettuce, black bean patties, tomato, and red onion. Serve immediately while the patties are warm and the edges are crisp.