Preheat the oven to 400 degrees F. Line 2 baking sheets with parchment paper.
Beat the egg in a shallow dish with 1 tablespoon water. In another shallow dish, stir together the Parmesan, garlic powder and some salt and pepper. Dip the green beans first in the egg mixture, rolling them to fully coat. Using a fork, gently transfer the green beans to the cheese mixture and roll to evenly coat them on all sides with the cheese.
Transfer the green beans to the prepared baking sheets, making sure the beans are in a single layer and not touching. Bake until golden brown and crisp-tender, about 10 minutes.