Peel the potatoes and carrots. Using a box grater with large holes, grate the potatoes, carrots, and zucchini.
Place the grated vegetables in a clean kitchen towel or cheesecloth and squeeze out any excess moisture.
In a large bowl, combine the squeezed vegetables, eggs, flour, garlic powder, smoked paprika, salt, and pepper.
Heat the oil in a large skillet over medium-high heat.
Form the vegetable mixture into small patties and carefully place them in the hot oil.
Fry the rostis for 3-4 minutes on each side, or until golden brown and crispy.
Transfer the cooked rostis to a paper towel-lined plate to drain excess oil.
Drizzle with BBQ sauce before serving. Serve hot.
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