Roll up grated zucchini in large kitchen towel; press to dry.
Heat oil in large deep skillet over high heat. Add 1 cup green onions and sauté 30 seconds. Add zucchini, carrots, and 2 tablespoons dill. Sauté until vegetables are just tender, tossing often, about 8 minutes. Mix in remaining 1/2 cup green onions and 2 tablespoons dill. Season to taste with salt and pepper.
