Grate the potatoes and carrots on the large holes of a box grater and transfer to a large colander set over a bowl. Grate the onion and add to the colander. Sprinkle with 1 teaspoon salt and 1/2 teaspoon pepper. Firmly squeeze the mixture with your hands to extract as much liquid as possible; blot dry on paper towels if especially wet. Transfer the mixture to a large bowl. Mix in the beets and parsley. Add the flour and egg and stir until thoroughly combined.
Line a baking sheet with paper towels. Working with 1/4 cup of the mixture at a time, form tightly packed pancakes 3 to 4 inches wide and transfer to the prepared baking sheet.
Heat 1/4 inch of vegetable oil in a large nonstick skillet over medium heat until shimmering. Working in batches, fry the pancakes until golden brown and crisp, 4 to 5 minutes per side. Transfer to a baking sheet and put in the oven while cooking the remaining pancakes.
Serve with sour cream.
Copyright 2016 Television Food Network, G.P. All rights reserved.