Mix the wet ingredients: Add the active sourdough starter, lukewarm water, honey, and melted butter to a large bowl. Stir until combined.
Add flour and salt: Mix in the flour and salt until a rough, slightly sticky dough forms. Cover and let it rest for 20–30 minutes.
Knead the dough: Knead by hand for 5–8 minutes, or use a stand mixer until the dough becomes smoother and more elastic. Avoid adding too much extra flour.
First rise: Place the dough in a lightly greased bowl, cover, and let it ferment at room temperature until noticeably puffy and lighter. This usually takes about 4–7 hours, depending on starter strength and room temperature.
Divide the dough: Transfer the dough to a lightly floured surface and divide it into 12 similar-sized pieces.
Shape the breadsticks: Roll each piece gently into an 8–10-inch rope. If the dough keeps shrinking back, let it rest for 5–10 minutes before rolling again.
Final rise: Place the shaped breadsticks on a parchment-lined baking sheet. Cover loosely and let them rise for about 1–2 hours, until slightly fuller and relaxed.
Make garlic butter: Mix the melted butter, grated garlic, Italian herbs, and salt in a small bowl.
Bake: Preheat the oven to 400°F (200°C). Brush the breadsticks lightly with garlic butter and bake for 15–20 minutes, or until lightly golden and baked through.
Finish: Brush the hot breadsticks with the remaining garlic butter. Add parsley and Parmesan if using. Serve warm.