Preheat oven to 450 F. Mix together water, sugar and yeast. Let sit for 10 minutes until it becomes foamy. In a separate bowl, combine the salt, Italian seasonings and garlic powder with 2 cups of the flour (see Cook’s note). Place the softened butter in with the yeast mixture; then add the flour mixture. Combine with your hands, and knead onto a lightly floured surface, adding the additional cup of flour if needed. Knead the dough for about 5 minutes or until it is smooth and elastic. Divide the dough in half. Cut each portion into 12 pieces, and roll each piece into a 4- to 6-inch rope. Place them about 2 inches apart onto a lightly greased baking sheet. Cover and let rise in a warm place for about 20 minutes or until doubled. Bake at 350 F, for 15 minutes or until golden brown. Immediately brush with the topping mixture, and sprinkle with the Parmesan cheese.