Finely grate the potatoes, onion, carrots, and zucchini into a large bowl. Set aside for 20 minutes. Drain off any excess liquid. Mix in the egg and garlic cloves. Season with salt, paprika, and black pepper. Add potato flour and stir with a wooden spoon until well combined.

Heat a large pan over medium heat and add 2 tablespoons vegetable oil. Pour the batter by tablespoons into the pan, making a few pancakes at a time. Cook about 2 minutes on each side until golden brown. Add the remaining oil to the pan, as needed. Using a spatula, transfer pancakes to a plate lined with paper towels. Repeat until all batter is used.

When all the pancakes are ready, transfer to serving plates and garnish with basil leaves.