Rinse veggies under cool running water then pat dry. Peel and grate parsnip, sweet potato, Yukon golds and onion. This is best accomplished using a food processor with a grater attachment—otherwise, the old fashioned way will do!
Place grated veggies in a large bowl then toss in chopped parsley. Sprinkle with salt, tossing to combine. Set mixture aside for at least 10 minutes to let salt to draw out excess moisture.
Transfer shredded veggies to a colander then press firmly to remove as much liquid as possible. Removing excess water will result in crispier patties. Transfer veggies back to mixing bowl then add flour, paprika, garlic powder, pepper and beaten egg. Mix thoroughly then set aside.
Place large skillet over medium heat. Add enough oil to coat bottom of pan by ¼". When oil is hot, form patties using a heaping ¼ cup of veggie mixture. Gently place patties in hot oil then fry 2–3 minutes per side—or until deep golden brown and crispy. Transfer to a paper towel-lined plate, sprinkle with a little extra salt and enjoy.
Remember—drawing excess moisture out of the grated veggies using salt is the best way to get crispy (not soggy) veggie patties!