Peel the beets and shred with the shredder attachment of a food processor. Remove shredded beets from machine into a large bowl.
Switch to the S blade and pulse the walnuts until crumbly, but not so long that they turn into butter.
Add the onion, garlic, beans, quinoa, and shredded beets and pulse 15-20 times until the mixture comes together but still has a slightly chunky texture and looks eerily like ground beef.
Transfer back to the mixing bowl and add the remaining ingredients.
Use your hands to squish everything together so it's evenly incorporated.
Refrigerate bowl for 30 minutes
Preheat your cooking surface(I like well-seasoned cast iron), if cooking right away, and shape into patties, either by hand or using a cookie cutter.
If your cast iron is well-seasoned, you will need very little or no oil. If not, use a light spray or swipe with a neutral high-heat oil like canola.
Cook for approximately 12 minutes, flipping a few times on each side until they are just barely charred and heated through.
Serve with all your favorite burger fixings!