If using canned black beans, drain and rinse them; if using pre-cooked beans, drain any excess liquid.
Add the drained beans, 1/2 cup cooked quinoa, 1 cup shredded beets, 1/2 red onion (diced), 2 cloves garlic (minced), 1 teaspoon chili powder, 1 teaspoon smoked paprika, 1 teaspoon kosher salt, and 1/2 teaspoon black pepper to a food processor. Pulse in short bursts until the mixture resembles coarsely ground meat, scraping down the sides as needed. Do not over-process into a smooth puree.
Transfer the mixture to a bowl and divide it into four even portions. Form each portion into a firm patty. If the mixture is too loose to form patties, refrigerate for 15–30 minutes to firm up, then reshape.
Choose one cooking method: - Stovetop: Heat the 1 tablespoon olive oil in a nonstick or well-seasoned skillet over medium heat. Add the patties and cook 6–8 minutes per side, until browned and heated through. - Oven: Preheat the oven to 375°F. Lightly oil a baking sheet with the 1 tablespoon olive oil or line it with parchment paper. Place the patties on the sheet and bake 10 minutes, flip, then bake an additional 10–15 minutes, until patties are firm and edges are lightly crisp.
Serve the burgers on a salad, in a bun, or plain.