Pulse the oats, cumin, chili powder, oregano, and beans in a food processor until a coarse puree forms. Add the pimentos, celery, parsley, and shallots. Pulse just until evenly distributed throughout. Form the mixture into 4 patties to match the diameter of the buns. Heat the oil in a large skillet over medium heat. Add the patties and cook, turning once, until crisp and browned on the outside and hot inside, about 10 minutes. Divide the greens and tomato slices among the bottom buns, top with the patties and sauce, and sandwich with the top buns.
For Toppings: Fold together the ingredients (for each topping separately) until well-mixed.