Grate your beets, onion and garlic using a box grater or food processor with grating blades. Place mixture into a bowl and mix in the egg, oats, and olive oil. Season with salt and pepper and let sit for 25 minutes to allow the oats to soak up some liquid.
While that sits, cut sweet potatoes into 1/4 inch slices lengthwise, and then cut those slices into strips to form a fry shape. Toss with some olive oil, garlic powder, salt and pepper.
Spread onto baking sheet and bake for 25 minutes, flipping half way through.
Heat a large saute pan over medium heat and drizzle with olive oil. Shape beet mixture into patties using hands and place into pan. Cook until golden on each side, about 4-5 minutes per side.
Remove fries from oven when done and let rest. Remove patties from pan and build your burgers with arugula and BBQ sauce.