1. Cream butter and granulated sugar until pale and fluffy.

2. Add egg, 2 teaspoons vanilla extract, and sourdough discard, mixing until combined.

3. Whisk all-purpose flour, baking powder, and salt in a separate bowl.

4. Gradually add dry ingredients to wet ingredients, mixing until a soft dough forms.

5. Divide dough into two disks, wrap, and chill in the refrigerator for at least 1 hour.

6. Preheat oven to 350°F and line baking sheets with parchment paper.

7. Roll dough to 1/4 inch thickness, cut shapes, and place cookies 1 inch apart on baking sheets.

8. Bake for 8 to 10 minutes until edges are just golden, then cool on a wire rack for 20 minutes.

9. Whisk powdered sugar, milk or cream, and 1/2 teaspoon vanilla extract until smooth.

10. Dip or drizzle cooled cookies with glaze and let set on a wire rack for 30 minutes.