Preheat oven to 325°F. Spread rinsed black beans on a parchment-lined baking sheet and bake for 15 minutes to dry out excess moisture.
Sauté bell pepper, onion, and garlic in olive oil over medium heat until softened, approximately 5 minutes. Drain any excess liquid.
Place dried beans in a large mixing bowl and mash with a fork until mostly broken down but still containing some whole bean pieces.
Incorporate the sautéed vegetables, cumin, chili powder, smoked paprika, breadcrumbs, feta cheese, eggs, Worcestershire sauce, ketchup, salt, and pepper into the bean mash.
Form the mixture into 4 uniform patties approximately 1 inch thick.
Heat a lightly oiled skillet over medium heat and cook patties for 4 to 5 minutes per side until browned and firm.
Serve immediately on toasted buns with preferred condiments.