Preheat the oven to 400°F and line a rimmed baking sheet with parchment paper.
Drain and rinse the beans, then pat them dry with a clean kitchen towel. In a large bowl, mash 2 cups of the beans with a fork until mostly smooth, leaving some chunky pieces, then stir in the remaining beans.
Add the oats, egg, onion, garlic, cumin, smoked paprika, salt, and pepper. Mix until evenly combined, then let the mixture rest for 5 minutes so the oats absorb moisture.
Divide the mixture into 4 equal portions and shape each into a patty about 3/4 inch thick. Brush both sides lightly with olive oil and place the patties on the prepared baking sheet.
Bake for 10 minutes, then flip each patty carefully with a thin spatula and bake for 10 minutes more, until firm to the touch and browned at the edges.
Let the patties rest for 5 minutes, then serve on toasted buns with lettuce, tomato, and avocado if you like.
