Make the Dough: In a large bowl, combine the warm water, instant yeast, and sugar. Let sit for 5 minutes until foamy. Add flour and salt, mixing until a soft dough forms. Knead for 5–7 minutes until smooth and elastic.
Let It Rise: Place the dough in a lightly oiled bowl, cover, and let rise in a warm spot for 45–60 minutes, or until doubled in size.
Shape the Breadsticks: Preheat oven to 375°F (190°C). Punch down the dough and roll it into a rectangle, about ½ inch thick. Cut into strips (about 12 pieces). Place them on a greased or parchment-lined baking sheet.
Brush with Butter: Melt the salted butter and brush it over the breadsticks. In a small bowl, mix the granulated sugar and cinnamon, then sprinkle evenly over the breadsticks.
Bake: Bake for 12–15 minutes, until golden brown and cooked through.
Make the Glaze: While the breadsticks bake, whisk together powdered sugar, milk, and vanilla until smooth. Adjust milk for desired consistency.
Finish and Serve: Drizzle the glaze over warm breadsticks. Serve immediately for the best texture.