In the bowl of a standing mixer, add the warm water, yeast and sugar. Mix gently, and let sit for a few minutes until it starts to get bubbly.
Once the yeast has started to get bubbly, add half of the flour, the salt, and the vegetable oil to the mixing bowl. Mix on low using the dough hook until all ingredients are well combined. Add the other half of the flour in ½ cup at a time until it has all mixed in. The dough should look smooth and pull away from the sides of the mixing bowl, but still be slightly sticky. If you need to, you can add a touch more flour or a touch more water to get it just right. Continue to mix on low for about 2 minutes.
Turn off the mixer and cover the bowl with a kitchen towel. Let sit for about 20-30 minutes, or until double in size.
Preheat the oven to 400 degrees.
Once the dough has doubled in size, sprinkle a little flour onto your counter and scoop the dough out onto it. Cut the dough into 16 equal pieces, and gently cover the pieces that you aren't shaping with your kitchen towel.
Lightly spray a baking sheet. Roll each piece into a 6-7" breadstick, and transfer it to the prepared baking sheet. (Note: If the dough isn't stretching very well, put it down and let it rest while you roll and stretch another breadstick)
Continue with all the breadsticks until they are all about the same size. Leave about 1-1.5" between each breadstick on your baking sheet.
In a small bowl, mix together the garlic powder and salt. Brush the melted butter onto each of the breadsticks using a pastry brush, then sprinkle with the garlic salt. Let the breadsticks rise until they are barely touching, and about double in size (another 20-30 min).
Bake at 400 degrees for 10-12 minutes, or until the breadsticks are lightly golden on the bottom. Remove from the oven and brush again with butter. Serve warm, and enjoy!