To prepare the burgers:Preheat oven to 350 degrees Fahrenheit.
Poke the sweet potato with a fork and cook in the microwave until tender, about 5 minutes. Set aside.
Peel the beets and shred them with a box grater. Place shredded beets into a large mixing bowl.
Puree walnuts in a food processor until finely ground - about the texture of couscous.
Peel the skin off the sweet potato and mash in a small bowl with a fork. Toss into the mixing bowl with the beets.
Add egg, onion, paprika, garlic, vinegar, Worcestershire, and ground walnuts to the beets. Stir well.
Form into six 4-inch patties and place on a greased cookie sheet. Bake for 20-25 minutes or until the begin to darken in color.
To prepare the aioli: Pplace egg yolk into a food processor with a pour spout and run on high speed. Combine the canola and olive oil into a measuring glass and pour a slow, steady stream into the food processor while it is still running. (The slower you add to start, the better.)
Continue to add the oil until the mayo starts to thicken. If it isn't thickened to your liking after adding the initial cup of oil, add up to 1/4 cup more.
Now, add the vinegar, sriracha, and garlic to your aioli in the food processor. Puree for a couple of pulses and serve!
Assembly:Assemble burgers by placing a beet patty on top of one half of the bun and topping with 1 tablespoon of aioli, lettuce, tomato, avocado, etc.