Activate the yeast: In a small bowl, combine the warmed milk, sugar, and yeast. Let it stand for 5 minutes until frothy.
Prepare the pan: Line a baking sheet with parchment paper and set aside.
Mix the dough: In a medium bowl, mix the flour and salt. In a large bowl, stir together the sourdough discard, 4 tablespoons of melted butter, and the milk mixture. Gradually add the dry ingredients and mix until a shaggy dough forms, ensuring no dry spots remain.
Let it rise: Pat or roll the dough out on the prepared parchment paper into a 9x9-inch square. Transfer to the baking sheet and let it rise in a warm spot for 30 minutes. Preheat your oven to 375ºF during this time.
Add the topping: Stir together the remaining melted butter, brown sugar, and cinnamon in a small bowl. Spread the mixture evenly over the dough. Use a knife or a dough cutter to slice the dough into 12 rectangles.
Bake: Bake the breadsticks for 15-20 minutes, or until puffed and golden brown. If needed, re-slice the sticks before serving.
Make the glaze: Microwave the cream cheese in a small microwave-safe bowl for 15-20 seconds until softened. Stir in the powdered sugar, milk (start with 2 teaspoons), and vanilla extract until smooth and drizzle-ready.
Serve warm: Drizzle the glaze on top of the breadsticks and enjoy them fresh out of the oven.