Preheat oven to 400°F and line a large baking sheet with parchment paper.
Slice zucchini into uniform sticks and pat them dry with a paper towel to ensure they get crispy.
In a shallow bowl, whisk the egg; in another bowl, combine parmesan, almond flour, garlic powder, oregano, salt, and pepper.
Dip each zucchini stick into the egg, then dredge in the parmesan mixture, pressing firmly to coat.
Season the chicken breast with olive oil and any remaining herb mixture, then place it on the baking sheet alongside the zucchini.
Bake for 20-25 minutes, flipping the zucchini halfway through, until the chicken reaches 165°F and the fries are golden brown.