Activate the yeast: In a large bowl (or the bowl of a stand mixer), combine the warm water, yeast, and sugar. Stir gently. Cover and let sit for 5 to 10 minutes, until foamy on top.
Make the dough: Add the melted vegan butter and salt to the yeast mixture. Stir to combine. Gradually add the flour, mixing until a soft dough forms. It should be slightly sticky, but still easy to handle.
Knead: Knead the dough on a lightly floured surface for 8 to 10 minutes, until smooth and elastic. (Or knead in a stand mixer with a dough hook for 5 to 6 minutes.)
First rise: Place the dough in a lightly greased bowl. Cover and let rise in a warm spot for 1 to 1½ hours, until doubled in size.
Shape the breadsticks: Lightly punch down the dough and use a knife to cut the dough into 12 equal pieces. Gently roll each piece into a rope about 7 to 8 inches (18 to 20 cm) long. Place on a parchment-lined baking sheet, spacing them about 2 inches apart.
Second rise: Cover loosely and let rise for 30 to 45 minutes, until puffy.
Bake: Preheat the oven to 400°F (200°C). Bake for 10 to 12 minutes, until lightly golden on top.
Finish with garlic butter: Immediately brush the warm breadsticks with melted vegan butter, then sprinkle evenly with garlic powder and salt. Serve warm.
