Preheat oven to 375 degrees F, and line a baking sheet with foil or parchment paper. If using foil, coat with cooking spray.
Add beans to a large bowl and mash with the back of a fork, keeping a few beans whole. Add grated beet.
Heat 1 tablespoon olive oil in a small skillet and cook onion for about 3 minutes, until it just begins to soften. Add onion to the bowl with beans and grated beets.
Pulse ½ cup old fashioned oats in the bowl of a small food processor, until they reach an almost flour-like consistency. Add to the burger mixture, along with 1 egg, 1 tablespoon apple cider vinegar and all of the spices.
Stir mixture well. Mix with my hands (disposable gloves are helpful here) to get it combined.
For 4 patties: Measure about ¾ cup of mixture to form a patty. For 6 patties: Measure about ½ cup of mixture to form each patty.
Place patties on the foil-lined pan and bake for 20 minutes on the middle rack of the oven. Flip and return to the oven for 18 to 20 more minutes, until cooked through.
Serve, as desired. Leftover patties can be refrigerated for up to 5 days.