In the bowl of a standing mixer, whisk together warm water, sugar, salt, and 3 tablespoons of melted butter.
Sprinkle yeast over the water mixture and let it sit for 5-10 minutes until foamy.
Whisk foamy yeast into the water mixture.
Combine flour and salt, then add to the liquid ingredients.
Use the bread hook attachment on low speed, gradually increasing to high once flour is fully mixed.
Knead the dough in the mixer for about 5 minutes until smooth and elastic.
Transfer dough to a large bowl coated with olive oil. Cover with plastic wrap and let it rise in a warm, draft-free place until doubled in size (60-90 minutes).
Punch down the dough and divide into twelve pieces (about 2 oz. each). Roll each piece into a rope the width of your thumb.
Place shaped breadsticks on parchment-lined baking sheets, 2-3 inches apart. Cover and let rise again for about an hour.
Preheat oven to 400°F. Bake breadsticks for 12-15 minutes until golden brown.
While baking, re-melt remaining butter if it has solidified.
Once out of the oven, brush breadsticks generously with melted butter and sprinkle with garlic salt.
Serve warm and enjoy!