Preheat oven to 350 degrees Fahrenheit.

Using a peeler, peel the zucchini into long, thin vertical strips.

In a bowl, combine red wine vinegar, olive oil, brown sugar, Dijon mustard, garlic, dill cubes, and pepper. Add zucchini strips and marinate for five to 10 minutes.

Place mayonnaise in a shallow bowl. Place panko crumbs and dried parsley in a second shallow bowl.

Remove one zucchini strip from the marinade. Lay on top of one chicken cutlet. Roll up tightly. Dip chicken roll-up in mayonnaise, then coat in crumbs. Place in a baking pan. Repeat with remaining chicken. Reserve the zucchini marinade.

Cover and bake for 30 minutes, covered.

Remove from oven and pour reserved marinade over each piece. Serve immediately.