Preparation:

Prepare the batter:  Pour the water into a medium mixing bowl. Stir in the yeast until dissolved. Let stand, covered 5 minutes. Stir in the olive oil, then whisk in the flour and 1 teaspoon salt. Continue whisking until the batter is nearly smooth, with only a few small lumps remaining. Cover the bowl loosely with a kitchen towel and let stand at room temperature 30 minutes to 1 hour.

Prepare the blossoms: Cut the stems of the flowers to 1 inch. Toss the mozzarella, Parmesan cheese, anchovy and 1/4 teaspoon pepper in a small bowl until mixed. Working with the flowers one at a time, dredge the ends lightly in flour. Gently open the flower, taking care not to tear it. Fill each flower loosely with about 1 1/2 tablespoons of the cheese mixture, placing the cheese toward the base of the flower and folding the ends over to completely enclose the cheese. Turn each stuffed flower in the flour until completely coated. Gently tap off excess flour and place the flower on a wire rack. repeat with remaining flowers. Pour enough oil into a heavy large skillet to a depth of 1 inch.  Heat over medium heat until a drop of batter sizzles instantly when added to the oil. Meanwhile, add half the flowers to the bowl of batter and turn until each is coated on all sides. Remove the flowers to a plate, wiping off excess batter against the side of bowl. Slip the coated flowers carefully into the oil. Fry, turning once, until deep golden brown on all sides, about 3 minutes. While the first batch of flowers are frying, coat and remove the second batch. Remove the flowers from the oil with a slotted spoon and transfer to a plate lined with paper towels. Let the oil reheat 30 seconds and fry the remaining flowers.  Sprinkle the flowers with salt and serve immediately.