Preheat the oven to 400 degrees F. Arrange two racks evenly spaced in the oven. Line two sheet pans with parchment paper.
Cut each zucchini in quarters lengthwise through the stem and then cut each quarter again in thirds lengthwise, making long skinny spears. In a medium shallow bowl, whisk together the pesto and 4 tablespoons of the olive oil and set aside. Place the parsley and garlic in the bowl of a food processor fitted with the steel blade and process until they are finely minced. Add the panko, Parmesan, red pepper flakes, 1 teaspoon kosher salt, and 1/2 teaspoon black pepper plus the remaining 4 tablespoons olive oil. Pulse only until all the panko is moistened with oil. Pour the mixture onto a dinner plate.
Dip the zucchini spears first into the pesto mixture, turning to coat completely, then place each one in the crumb mixture, pressing and turning to coat thickly. Arrange the sticks in rows on the prepared sheet pans.
Roast for 20 to 30 minutes, until the zucchini is tender and the crumbs have crisped to a crunchy golden brown. Sprinkle lightly with flaked sea salt and serve hot.