Prepare the Dough:
In a bowl, combine warm water, sugar, and yeast. Allow it to sit for 5-10 minutes until foamy.
In a large mixing bowl, combine flour and salt. Make a well in the center and pour in the yeast mixture and olive oil.
Mix until a dough forms. Knead on a floured surface for about 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm place until doubled in size (approximately 1 hour).
Shape and Bake the Breadsticks:
Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper.
Punch down the risen dough and divide it into golf ball-sized portions. Roll each portion into a rope shape and place on the prepared baking sheet.
In a small bowl, mix melted butter, minced garlic, and chopped parsley. Brush the garlic butter blend over each breadstick.
Bake for 15-18 minutes or until golden brown.
Add the Cheese Topping:
Sprinkle shredded mozzarella and grated Parmesan evenly over the baked breadsticks.
Return the breadsticks to the oven and bake for an additional 5-7 minutes or until the cheese is melted and bubbly.