Preheat oven to 400F. Prepare a baking sheet with tin foil or parchment paper.
Cut zucchini into ½ inch fries. In a large bowl, soak the zucchini in 1 cup of buttermilk. Meanwhile, mix together panko, parmesan, 1 tsp celery salt, salt and pepper in a bowl. Roll wet zucchini in the dry mixture to get a good coating. Place on the baking sheet in a single layer and brush with olive oil. Bake for 40 minutes, turning halfway through.
While the fries are baking, add all of the ingredients for the dipping sauce (yogurt, buttermilk, dill, chives, 1/2 tsp celery salt, salt, and pepper) in one bowl and mix until smooth.
Sprinkle fresh parsley over cooked fries and serve with dipping sauce.