For the dough, pour the water into a stand mixer with the sugar and yeast, and let that sit and froth for about 10 minutes. Add salt, butter, and 2 cups of flour. Mix the dough on low. Using the dough hook, add the rest of the flour a half cup at a time, until dough scrapes the sides of the bowl clean. Mix the dough about 5 minutes on medium speed, until it is soft and easy to work with.
Let the dough rest in the bowl (covered) until doubled in size, about 1 hour. Preheat the oven to 170 degrees. Roll the dough out into a long log, spray a knife with cooking spray and cut the dough into 12-14 pieces. Roll those pieces into about 6 inch long snakes. Spray 2 large cookie sheets with cooking spray, and lay the breadsticks out leaving about 2 inches between each one.
Place them in the oven and let them rise for about 15 minutes, or until doubled in size. (If you are not in a hurry, you could let them sit at room temperature until they are doubled in size and then proceed with the baking step.)
Melt 3 tablespoons of butter in a bowl. Once risen, brush breadsticks with about half of the melted butter and sprinkle them liberally with salt. Preheat the oven to 400 degrees and bake them for 12-14 minutes or until golden brown.
While they are baking add 1 teaspoon garlic powder to the remaining butter (about 1 and 1/2 tablsepoons). When the breadsticks are golden brown, remove them from the oven and brush them with the butter/garlic mixture.