Line two baking trays with parchment paper.
In a medium bowl, stir together flour, salt, sugar, and instant yeast. Add warm water, melted butter (⅓ cup), and beaten eggs. Mix until a dough forms.
Transfer dough to a clean, lightly floured surface. Shape into a round, cut in half, and cover one half.
Split dough into 5 equal pieces and shape each into a breadstick log. Transfer to baking trays.
Let dough rest while preheating oven to 375°F. Bake breadsticks for 10-15 minutes until golden.
While baking, combine remaining melted butter (3 tbsp), Parmesan, and garlic powder for the topping.
When bread comes out of the oven, generously brush with garlic butter and serve hot.