In a small, shallow bowl, combine the panko, zests, and 1 tablespoon of oil. Place the remaining 1/2 cup of oil in another small bowl.
Slice or shape the chèvre into eight 1-inch-thick disks. One disk at a time, dip both sides into the oil and then the panko mixture, pressing gently on both sides and all edges so the crumbs adhere. Arrange the coated disks on a rimmed baking sheet and place in the freezer until frozen, about an hour.
Preheat the oven to 400°F.Transfer the baking sheet to the oven and bake until the panko is lightly golden, about 15 minutes.
Meanwhile, in a large bowl, toss the greens with dressing to taste. Arrange the greens on plates or a platter.
Carefully arrange the baked cheese on the greens and serve.
