In a food processor, coarsely grate beets, carrots, and onion. Transfer to medium bowl.
Add eggs, flour, salt, and pepper; stir to combine.
Fried method:
In a large skillet, add evoo until depth reaches ½ inch, and heat over medium-high heat. Spoon ¼-cup sized scoops of latke mixture into the pan, and flatten with the back of a spoon or spatula. Fry until golden, 4-6 minutes per side. Remove to a paper towel-lined plate to drain.
Baked method:
Preheat oven to 450°F. Place ¼-cup sized spoonfuls of the prepared latke mixture on a cookie sheet lined with parchment and coated with evoo. Flatten each latke with the back of a spatula.
Bake for 10 minutes. Flip the latkes and bake for another 10 minutes, until crisp and golden.