Preheat the oven to 350 degrees Fahrenheit.
In a small saucepan, combine the rinsed quinoa and vegetable broth. Bring to a simmer and cover. Continue to simmer until broth is absorbed and quinoa is tender, about 15 min.
Poke the sweet potato with a fork on all sides. Place in the microwave and cook until fork tender. Set aside to cool and then remove the skin.
Place oats in a food processor or the single serving blender cup and puree until flour consistency.
Combine the flax seeds and water in a small bowl and stir. Set aside.
Add the beans to the food processor and pulse 6-8 times to break apart most of the beans. (Aim for the consistency of refried beans.)
In a large mixing bowl, combine the quinoa, peeled sweet potato, 1/4 cup + 1 tablespoon of the ground oats, soaked flax, beans, and seasonings. Stir to combine well. Wet your hands with water and form dough into 3-4" patties. Place patties on a greased baking sheet.
Bake burgers for ~25-35 minutes or until lightly browned and crisp on the outside. Flip burgers halfway through cooking.