Place the grated potatoes in a colander and squeeze out excess moisture using a clean kitchen towel or cheesecloth.
In a large bowl, combine the grated potatoes, chopped onion, minced garlic, eggs, flour, caraway seeds (if using), paprika, salt, pepper, and chopped parsley. Mix until well combined.
Heat a generous amount of vegetable oil in a large skillet over medium heat.
Spoon a portion of the potato mixture into the hot oil, flattening it into a round pancake shape with the back of the spoon. Fry until golden brown and crispy on both sides, about 3-4 minutes per side.
Remove the cooked bramboráky from the skillet and drain on paper towels to remove excess oil.
Enjoy your meal!