In a large mixing bowl, combine the warm water, sugar, and yeast. Let this mixture sit for about 5 minutes, or until it becomes frothy.
Once the yeast is activated, add the softened butter and salt to the bowl. Gradually stir in the all-purpose flour, one cup at a time, until a soft dough forms.
Transfer the dough to a lightly floured surface and knead for about 5-7 minutes until it becomes smooth and elastic.
Place the kneaded dough in a lightly greased bowl, cover it with a kitchen towel, and let it rise in a warm area for about 1 hour, or until it has doubled in size.
After the dough has risen, punch it down to release any air bubbles. Divide the dough into 12 equal pieces. Roll each piece into a long, thin strip, about 6 inches long, and place them on a baking sheet lined with parchment paper.
Cover the shaped breadsticks with a kitchen towel and let them rise again for about 30 minutes.
Preheat your oven to 400°F (200°C). Once the breadsticks have risen, bake them in the preheated oven for about 12-15 minutes, or until they are golden brown.
Remove the breadsticks from the oven and immediately brush them with melted butter mixed with garlic powder and sea salt.