1. Preheat oven to 350°F (175°C) and line baking trays with parchment paper.

2. In a large bowl, beat softened butter and granulated sugar (and brown sugar if using) until pale and fluffy.

3. Add sourdough starter discard and the egg, mixing until fully combined.

4. Stir in vanilla extract.

5. In a separate bowl, whisk together flour, baking soda, and salt.

6. Gradually mix dry ingredients into the wet mixture until no flour streaks remain.

7. Adjust dough texture with extra flour or a teaspoon of milk if needed.

8. Cover dough and refrigerate for at least 30 minutes.

9. Use a cookie scoop to portion dough into 1-inch rounds, spacing 2 inches apart on trays.

10. Bake for 9–11 minutes until edges are light golden; allow to cool on trays for 5 minutes, then transfer to a cooling rack.

11. In a small bowl, whisk powdered sugar, vanilla extract, melted butter, and milk until smooth and pourable.

12. Dip or drizzle cooled cookies with glaze and let set for 15–20 minutes.

13. Store cookies in an airtight container at room temperature for up to 5 days, adding a bread slice to maintain softness.