Cream the butter and sugar. In a large bowl, beat the softened butter and granulated sugar until light and fluffy, about 2–3 minutes. This traps air and helps your cookies bake up tender.

Add the egg and flavorings. Beat in the egg, vanilla, and any other extracts until smooth. Scrape the bowl so everything blends evenly.

Mix in the sourdough discard. Stir in the discard until fully combined. The mixture may look slightly curdled at first, but it will smooth out.

Whisk dry ingredients. In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.

Combine wet and dry. Add the dry ingredients to the butter mixture in two additions. Mix on low just until no dry spots remain. Do not overmix.

Chill the dough. Divide the dough into two portions. Flatten into discs, wrap in plastic, and chill for at least 45 minutes (or up to 48 hours). Chilling helps flavor and shape.

Preheat and prep. Heat the oven to 350°F (175°C). Line baking sheets with parchment.

For rolled cookies: Lightly flour your surface. Roll the dough to about 1/4 inch thick. Cut shapes with cookie cutters, re-rolling scraps as needed.

For drop cookies: Scoop 1 1/2 tablespoon mounds, roll into balls, and dip tops in sugar if you like. Space them 2 inches apart.

Bake. Bake 8–10 minutes for drop cookies or 9–12 minutes for cut-outs, depending on size. Edges should be set and just starting to color; centers will look pale.

Cool. Let cookies rest on the sheet for 5 minutes, then transfer to a rack to cool completely. They’ll firm up as they cool.

Optional icing. Whisk 1 cup powdered sugar with 1–2 tablespoons milk, a splash of vanilla, and a tiny pinch of salt. Drizzle or spread on cooled cookies. Add sprinkles right away.