In a mixing bowl, mash black beans. Add rice, beets, oats, onion, egg white, smoked paprika, salt, and pepper to the beans and fold until all is combined. Form into 2 patties.
Heat olive oil in a skillet over medium heat. Add patties to the skillet, cover, and let cook for 5 minutes on each side.
Divide salad greens between two serving dishes and top with an equal amount of the tomatoes, cucumber, and carrots. Serve veggie burger over salad. Drizzle with a low-calorie dressing or vinegar, if desired.
Combine 1/4 cup nonfat plain Greek yogurt with 2 tablespoons of pesto sauce for a quick dressing for 2.