In the bowl of a stand mixer fitted with the paddle attachment, combine warm water, yeast, and sugar. Let it sit for 5–10 minutes, or until the yeast is bubbly and foamy.
Add salt, oil, and bread flour. Mix on low speed until a shaggy dough forms. If the dough is too sticky, add a little more flour, one tablespoon at a time, just until the dough pulls away from the sides of the bowl.
Switch to the dough hook attachment and knead the dough on medium speed for about 5 minutes, or until smooth and elastic.
Lightly grease a medium bowl with olive oil or nonstick spray. Shape the dough into a ball and place it in the bowl. Cover with a clean kitchen towel or plastic wrap and let rise in a warm spot for about 1 hour, or until doubled in size.
Line two large baking sheets with parchment paper.
Once the dough has risen, gently punch it down to release the air. Transfer it to a lightly floured surface. Divide the dough into 12 equal pieces. Roll each piece into a ball, then roll each ball into a rope about 9 inches long.
Place the dough ropes evenly spaced on the prepared baking sheets. Cover loosely with a clean kitchen towel and let rise again for about 1 hour, or until slightly puffy.
Preheat the oven to 425°F.
Bake the breadsticks for 12–15 minutes, or until golden brown.
While the breadsticks are baking, stir together the melted unsalted butter, garlic salt, and kosher salt in a small bowl.
Remove the breadsticks from the oven. While they are still warm, brush them generously with the garlic butter mixture.
Serve warm.