In a small bowl, dissolve the sugar and yeast in the water and let sit for 5 minutes, until it frothy and bubbly.
In a stand mixer bowl, combine 2 1/2 cups flour and salt. Using the paddle attachment, mix the softened butter into the flour until well combined. (If you don't have a stand mixer, simply mix ingredients together in a bowl using a large mixing spoon.)
Add the sugar and yeast mixture to the flour mixture. Using the dough hook, knead dough in the bowl for 8 minutes (if you don't have a mixer, feel free to knead by hand).
The dough may be sticky, so add more flour as needed or until the dough stops sticking to the sides of the bowl (at the most, add 1/2 cup - if you add more than that, your breadsticks won't turn out).
Cover the bowl with a towel and let dough sit for 1 1/2 hours or until it has doubled in size.
Once the dough has doubled, divide dough into 12 equal portions (if you want to weigh them, they will be about 2 ounces each). Roll into elongated shapes about 1 1/2" thick and 6-7" long.
Place the dough on baking sheets and cover with a towel. Let dough sit for 1 hour, until doubled again in size.
Preheat oven to 400 degrees F.
Bake breadsticks for 10 minutes or until they start to brown slightly.
Make the topping by combining the melted butter and garlic salt. When the breadsticks come out of the oven, brush them with the melted butter mixture using a pastry brush. Serve and enjoy!