Bloom the yeast: Stir warm water and sugar in a large bowl, sprinkle in yeast, and let it foam for 5–10 minutes.
Start the dough: Mix in 2 cups flour, the softened butter, and fine salt until shaggy.
Add remaining flour gradually, kneading until a soft, slightly tacky dough forms, 6–8 minutes by hand or mixer.
Grease a bowl with olive oil, place dough inside, turn to coat, cover, and let rise until doubled, about 1 hour.
Punch down the dough and divide into 12 equal pieces. Roll each into a 7–8 inch rope.
Arrange on a parchment-lined sheet, cover, and let rise 15–20 minutes while the oven heats to 400°F.
Bake until lightly golden, 12–15 minutes.
Combine melted butter with garlic powder and a pinch of kosher salt.
Brush hot breadsticks generously with the garlic butter. Sprinkle with remaining kosher salt and parsley.