Preheat your oven to 425°F (220°C).
In a small bowl, combine the olive oil, minced garlic, mixed dried herbs, lemon juice, salt, and pepper to make a marinade.
Coat the chicken breast evenly with the marinade. Let it rest while you prepare the zucchini sticks.
Slice the zucchini lengthwise into sticks. Place them in a bowl, drizzle a tiny bit more olive oil if desired, and toss with salt, pepper, and half of the shredded Parmesan cheese.
Arrange the zucchini sticks on a baking sheet lined with parchment paper, ensuring they are not overcrowded.
Place the chicken breast on another baking sheet. Bake both the chicken and zucchini sticks in the preheated oven.
Bake the chicken for about 18-20 minutes, or until its internal temperature reaches 165°F (74°C). Bake the zucchini sticks for 12-15 minutes until they turn golden and crispy.
About 5 minutes before the zucchini sticks are done, sprinkle the remaining Parmesan cheese on top for extra crispiness.
Once cooked, remove both dishes from the oven. Let the chicken rest for a few minutes before slicing.
Plate the chicken alongside the crispy zucchini sticks and serve immediately.