Preheat oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Place the shredded zucchini and shredded potato in a clean kitchen towel and squeeze forcefully to remove all excess liquid.
In a large mixing bowl, combine the dried zucchini, dried potato, beaten egg, breadcrumbs, Parmesan cheese, garlic powder, onion powder, salt, and pepper.
Mix thoroughly until the ingredients are evenly distributed and the mixture holds together when pressed.
Scoop 1 tablespoon of the mixture and compress it into a small cylinder shape using your hands.
Arrange the tots on the prepared baking sheet with at least 1 inch of space between each.
Lightly brush the tops of the tots with olive oil or spray with a non-stick cooking oil.
Bake for 25 minutes, flipping the tots halfway through the duration, until the exterior is golden brown and crispy.
Remove from the oven and let rest for 3 minutes before serving.