Heat the oven to 325°F. Line the baking sheet with parchment. Drain and rinse the black beans, then pat them thoroughly dry. Spread them in a single layer on the sheet and bake for 15–20 minutes, until their skins look wrinkled, some split and the surface appears dry. Avoid scorching. Set the sheet aside.

Heat 1 tablespoon of the olive oil in the skillet over medium heat. Add the onion and red pepper; cook for 8–10 minutes, stirring, until softened and the pan is mostly dry. Add the garlic for the last minute. Remove from the heat and allow to cool for 5 minutes. The beans and vegetables should no longer be hot before adding the egg.

Transfer the beans to the mixing bowl and roughly mash about two-thirds, leaving visible coarse pieces. Fold in the cooled vegetables, beaten egg, panko, cumin, smoked paprika, salt and pepper. Mix just until evenly combined rather than processing into a smooth paste.

Divide the mixture into 6 equal patties, approximately 4 inches across and 1/2 inch thick. Set them on the lined sheet and refrigerate for 20 minutes so they are easier to lift.

Wipe out the skillet if needed. Heat 1 tablespoon olive oil over medium heat. Add 3 patties with space between them and cook for 4–5 minutes per side, until a browned crust forms and the center reaches 160°F on an instant-read thermometer. Turn once with a wide spatula, waiting until the first side is firm enough to lift. Repeat with the final tablespoon oil and remaining patties; reduce the heat if the surfaces brown before the centers are hot.

Serve the patties promptly with buns and toppings if desired. Keep cooked patties separate from bread and wet toppings when storing leftovers.