Clean the flowers in cool water and dry with paper towels. Cut off the stems, reach inside the flower and pull out the pistil. Inside the flower, stuff 1/2 of an anchovy and a mozzarella ball. Repeat for remaining zucchini flowers.
Make the batter. Place flour in a medium bowl. Whisk in water, then add salt.
Heat fryer to 350°F. Dip each zucchini flower in the batter, then place in the fryer basket, working quickly. Fry for 1-3 minutes, or until just beginning to turn golden. Remove flowers and sprinkle with salt. Enjoy immediately.