Drain and rinse the canned black beans thoroughly. Place half of the beans (1 cup) in a large mixing bowl and mash with a fork or potato masher until mostly smooth but still some texture remains. Finely dice the onion and red bell pepper. Mince the garlic.

Process remaining beans and oats

Put the remaining 1 cup of black beans and the oats in a food processor and pulse 6–8 times until coarsely ground — mixture should be pasty but still have small bean pieces. If you don't have a processor, finely mash the second cup of beans and mix with extra oat flour.

Combine patty mixture

Add the processed beans/oats to the mashed beans bowl. Stir in the diced onion, red bell pepper, minced garlic, ground cumin, smoked paprika, chili powder, chopped cilantro, lime juice, hot sauce (if using), salt, and black pepper. Break the egg into the mixture (or add prepared flax egg) and mix until evenly combined. If mixture feels too wet, add up to 2 tbsp more oats; if too dry, add 1 tsp water or another small splash of lime juice.

Form patties

Divide the mixture into 4 equal portions (about 3/4 cup each). Shape each portion into a compact patty about 3/4-inch thick. Press the edges to hold together; refrigerate for 15–20 minutes to firm up if time allows.

Cook patties

Heat a large nonstick skillet over medium heat and add 1 tbsp olive oil. When oil is shimmering, add two patties (do not overcrowd). Cook 4–5 minutes per side until a dark golden crust forms and internal temperature reaches about 165°F (for safety) or patties feel firm. Add remaining 1 tbsp oil and cook the other two patties. If desired, finish patties in a 350°F oven for 5 minutes to fully set.

Burger Sauce

In a small bowl, whisk together mayonnaise, Greek yogurt, minced chipotle (or chipotle paste), lime juice, honey or maple syrup, garlic powder, smoked paprika, and salt until smooth. Taste and adjust seasoning — add more chipotle for heat or more lime for brightness. Refrigerate until ready to assemble.

Assembly & Garnish

Toast the burger buns cut-side down in a dry skillet or toaster until golden.

Spread about 1 tbsp of the burger sauce on the bottom bun. Place a lettuce leaf on the sauce, then a black bean patty. Top the patty with a slice of tomato, some red onion, and avocado slices if using. Drizzle another 1 tbsp of sauce on the top bun and place on the burger.

Repeat to assemble remaining burgers. Serve immediately with lime wedges on the side. Leftover patties can be refrigerated for up to 3 days or frozen for up to 1 month.