Heat the oil in a medium skillet over medium heat. Once oil is shimmering, add the onions and garlic and cook until onions are soft and translucent, about 5 minutes. Remove from heat and set aside.
In a large mixing bowl, add the white beans and mash with the back of a fork until mostly mashed. Add the cooked farro, cooked onion mixture, oat flour, chiles, cumin, chili powder, and mayonnaise.
Form the burgers into patties (about ½ cup per burger) and place on a baking tray lined with parchment paper. Once burgers are formed, heat the oil in a large skillet over medium heat. Once oil is shimmering, add the burgers in an even layer (you may need to work in batches.) Cook 5 minutes per side until firm and browned. If you want to top with cheese, top each burger with cheese slices, cover, and let the cheese melt, about 3 minutes. Transfer the burgers to buns and top with guacamole or desired toppings. Serve.