In a large bowl or the bowl of a stand mixer, combine ½ cup of the warm water, sugar, and active dry yeast. Stir gently and let sit for about 5 minutes until the mixture becomes foamy.

Add the remaining ¼ cup warm water, olive oil, salt, and white vinegar to the yeast mixture. Begin mixing on medium-low speed using the dough hook attachment, or use a wooden spoon if mixing by hand. Gradually add in the flour, about ½ cup at a time, until the dough starts to pull away from the sides of the bowl.

Knead for 4-5 minutes or until the dough is smooth and slightly sticky. Cover the bowl with a clean kitchen towel and let the dough rest in a warm place for 1 hour, or until it has doubled in size.

Preheat your oven to 475°F. Place a pizza stone or an upside-down baking sheet inside the oven to preheat.

Gently punch down the dough and transfer it to a large piece of parchment paper. Use your hands (or a rolling pin) to shape the dough into a rectangle about ⅓ inch thick.

In a small bowl, mix the melted butter and minced garlic together. Brush this garlic butter mixture evenly over the dough.

Top with a generous layer of freshly grated Parmesan cheese, followed by the shredded mozzarella cheese.

Carefully transfer the parchment paper with the dough onto the hot pizza stone or baking sheet in the oven. Bake for 8-12 minutes, or until the cheese is melted, bubbly, and golden-brown.

Remove the breadsticks from the oven and let them cool for a few minutes before slicing. Serve warm with your favorite dipping sauces like marinara, ranch, or garlic butter.