In the bowl of a stand mixer, whisk together warm water, yeast, and sugar. Let sit for 5–10 minutes until bubbly and foamy on top.
Whisk in the sourdough discard (make sure it’s at room temp) until well combined.
Add melted butter, salt, and bread flour. Mix on low speed using the dough hook attachment, then increase to medium until a smooth dough forms and pulls away from the sides. If too sticky, add more flour 1 tablespoon at a time.
Knead in the mixer for 10 minutes (or by hand on a floured surface) until soft and stretchy. The dough should be slightly tacky but manageable. This is the right dough consistency.
Form into a ball and transfer to a greased bowl, turning to coat all sides. Cover with a clean tea towel or plastic wrap. Let rise in a warm spot for 1 - 1.5 hours or until doubled in size.
Punch down the dough and divide it in half. Cut each half into 8 pieces. Roll each into a thin stick, about 6-8 inches long. Place on a sheet pan lined with parchment paper or silicone baking mats.
Cover and let the shaped dough rest for 20–30 minutes until puffy.
Preheat oven to 400°F (204°C). Bake the breadsticks for 17–19 minutes in a preheated oven, rotating pans halfway through, until golden with a slightly crispy bottom.
Mix the garlic butter topping. Brush warm breadsticks generously after baking. Sprinkle with parmesan cheese, poppy seeds, or herbs if you’d like!