1. 1. Prepare your wet ingredients: In a large mixing bowl, combine the active sourdough starter, granulated sugar, melted butter, egg, and vanilla extract. Whisk these ingredients together until they are well combined and smooth. The mixture should look slightly creamy.

2. 2. Combine dry ingredients: In a separate medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Make sure there are no lumps and the dry ingredients are evenly distributed.

3. 3. Mix wet and dry: Gradually add the dry ingredient mixture to the wet ingredients, alternating with the 1/4 cup of milk. Start and end with the dry ingredients. Mix until just combined. Be careful not to overmix; a few lumps are okay. The dough will be soft and slightly sticky.

4. 4. Shape the breadsticks: Lightly flour a clean surface. Turn the dough out onto the floured surface and gently knead it a few times, just enough to bring it together. Roll the dough out into a rectangle, about 1/2 inch thick. Using a pizza cutter or a knife, cut the dough into strips about 1 inch wide and 6-8 inches long.

5. 5. Bake the breadsticks: Preheat your oven to 375 F (190 C). Line a baking sheet with parchment paper. Arrange the breadstick strips on the prepared baking sheet, leaving a little space between each one. Sprinkle the cinnamon sugar generously over the tops of the breadsticks.

6. 6. Bake until golden: Bake for 15-20 minutes, or until the breadsticks are golden brown and cooked through. They should feel firm to the touch. Remove them from the oven and let them cool slightly on the baking sheet before transferring them to a wire rack.

7. 7. Prepare the dip: While the breadsticks are cooling, whisk together the powdered sugar, 1-2 tablespoons of milk, and 1/4 teaspoon vanilla extract in a small bowl until smooth. Add more milk a tiny bit at a time if you prefer a thinner consistency.

8. 8. Serve and enjoy: Serve the warm or room-temperature breadsticks with the prepared sweet dip on the side.