Combine the drained beans, quartered onion, rolled oats, chili powder, salt, pepper, and egg in a food processor. Pulse until the mixture is chunky and holds together but is not completely puréed. If it seems too dry, add a tablespoon of liquid.
Let the mixture rest for 5 minutes to allow the oats to absorb moisture.
With slightly wet hands, form the mixture into 4 to 6 evenly sized patties. For the firmest burgers, let the shaped patties rest in the refrigerator for 15-30 minutes, but you can cook them immediately if you're short on time.
Heat the oil in a large nonstick or cast-iron skillet over medium heat. Carefully place the patties in the skillet and cook for about 5 minutes per side, until they are nicely browned, crisp on the outside, and firm throughout.
Serve immediately on toasted buns with your favorite fixings like lettuce, tomato, onion, and a delicious sauce, or let them cool completely to refrigerate or freeze for later.