Preheat oven to 400°F. Line a baking sheet with parchment paper.
Shred carrot and zucchini. Use a clean towel or paper towel to squeeze out excess water from the zucchini.
In a large bowl, combine ground chicken, shredded carrot and zucchini, egg, oat flour, onion powder, garlic powder, cumin, salt, paprika, and pepper. Mix until fully combined.
Scoop tablespoon-sized portions of the mixture and shape into nuggets or small patties.
Place nuggets on the prepared baking sheet, leaving space between each one.
Bake for 10–15 minutes, or until the internal temperature reaches 165°F.
Let cool slightly before serving.