In a large strainer placed in the sink or over a plate, combine the potatoes and zucchini. With your hands, squeeze to remove any excess water. Add 3 tablespoons of the dill and toss. Heat the oil in a large cast-iron skillet over medium-low heat. Add the potato-and-zucchini mixture, pressing it with the back of a spatula. Season with the salt and pepper. Cook, without stirring, for 15 minutes. Fold the hash in half. Cook for a few more minutes. Transfer to individual plates along with the eggs. Sprinkle both the hash and eggs with the remaining dill.