Drain and rinse the black beans, spread them on a clean kitchen towel, and pat thoroughly dry. Transfer to a large mixing bowl and mash with a fork or potato masher until about two-thirds are broken down — leave some chunks for texture.

Stir in the onion, garlic, cumin, chili powder, smoked paprika, salt, and pepper. Add the eggs, 1/2 cup cotija, oat flour, and panko; mix until evenly combined. Let the mixture rest 5 minutes so the oats and panko hydrate and firm up.

Divide into 4 equal portions and shape into patties about 3/4 inch thick, pressing firmly so they hold. Press a shallow dimple in the center of each with your thumb (it keeps them from puffing).

Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering. Add the patties (don't crowd — work in batches if needed) and cook 4–5 minutes per side, until deep golden-brown with crisp edges. The egg binder must set fully: patties should feel firm, not soft in the center.

Wipe the skillet, add the remaining 1 tablespoon olive oil, and toast the buns cut-side down 1–2 minutes until golden.

Layer lettuce, a patty, avocado slices, salsa, and the remaining cotija on each bun. Squeeze lime over everything and serve immediately with extra lime wedges.