Preheat the oven to 425 degrees. Place a baking stone on a rack in the lower third of the oven. If you don't have a baking stone, use an over turned half sheet pan (if neither options are available, bake the breadsticks on the lowest rack in the oven). Allow the baking stone/baking sheet to heat at 425 degrees for at least 15-20 minutes before baking the breadsticks.
In a large bowl, stir together the warm water, yeast and sugar. Let sit for 3-4 minutes until foamy.
Add the salt and flour and stir together until the dough forms a shaggy ball. It should be soft and slightly sticky but not overly wet.
Knead the dough (right in the bowl) 15-20 times, greasing your hands or adding additional flour a tablespoon at a time, if needed. Don't over flour the dough; it should be soft and pliable.
Knead and pat the dough one final time into a ball, cover the bowl, and let the dough rise for 15-20 minutes until noticeably puffy.
Lightly grease a half sheet pan with nonstick cooking spray (or brush with melted butter).
Grab the dough from the bowl and stretch it out just a bit into a thick rectangle before placing on the sheet pan. Press the dough evenly into a large rectangle in the bottom of the sheet pan. (If the dough springs back or doesn't press out evenly, leave the dough alone and let it rest for 10-15 minutes to relax the gluten and then continue pressing it into a large rectangle.)
Brush the dough with the two tablespoons melted butter or olive oil. Sprinkle with the garlic herb seasonings.
Sprinkle the mozzarella cheese evenly over the top of the dough followed by the Parmesan cheese.
Bake immediately or let the dough rest for 10-15 minutes for slightly puffier breadsticks.
Place the sheet pan of breadsticks directly on the preheated pizza stone or over turned baking sheet, and bake for 15-17 minutes until the breadsticks are golden and the cheese is bubbly.
Cut the breadsticks in half lengthwise (the long way) and then cut into strips for about 18 breadsticks total.
Notes
Garlic Herb Seasoning: I use this garlic herb seasoning (I grab it at Costco; it's also at Walmart and online at Amazon). If you don't have store bought garlic herb seasoning, you can use the following ingredients: 1/4 teaspoon kosher salt + 1 teaspoon dried basil + 1 teaspoon dried oregano + 1/2 teaspoon garlic powder + 1/4 teaspoon dried thyme. Proofing the Yeast: technically you don't have to proof the yeast (let it get foamy in the warm water) before adding the flour. You can add all the dough ingredients and mix right off. But I've found that because this dough has a quick rising time, letting the yeast proof in the water for just a few minutes before adding the salt and flour gives it a jump start so the breadstick dough rises well during the short rising time.