Cook quinoa and boil potatoes at the same time.
When quinoa is done and potatoes are tender, drain and mash the potatoes until mostly smooth. Some chunks are ok.
Drain the black beans and empty half of the can into a large bowl. Mash the beans using a fork, then add the remaining whole beans.
Add in 3 cups mashed sweet potatoes, quinoa, red onion, and seasonings and mix to combine.
Add eggs, bread crumbs, and brown rice flour and mix well.
Preheat the oven to 400º and line two baking sheets with parchment paper.
Scoop out the mixture into 1/4 – 1/3 cup amounts and use your hands to shape it into small "disks" about 3/4" thick.
Repeat the process until your baking sheets are full or you run out of the mixture.
Bake 25 minutes, flipping the cakes once near the halfway point.
