Prep: Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
Cream Butter & Sugar: Beat butter and sugar until light and fluffy, 2–3 minutes.
Add Wet Ingredients: Mix in egg, sour cream, sourdough discard, and vanilla (plus almond extract if desired) until smooth.
Whisk Dry Ingredients: In a separate bowl, whisk together flour, cornstarch (or arrowroot), baking powder, baking soda, cream of tartar, and salt.
Combine: Gently fold dry into wet until just combined. Dough will be soft and slightly sticky.
Chill Dough: Wrap in parchment or place in a zip-top bag. Refrigerate at least 2 hours (up to 3 days) for best texture.
Shape: Scoop 2-tablespoon portions, roll into balls, place on baking sheet, and slightly flatten tops.
Bake: 9–11 minutes, until edges are set but centers are pale. Do not overbake.
Cool: Allow cookies to cool completely before frosting.
Frosting
Whip together butter, powdered sugar, milk, vanilla, and a pinch of salt. Add food coloring and sprinkles if desired. Spread over cooled cookies.