1. Preheat oven to 350°F and line two baking sheets with parchment paper.
2. Cream butter and sugar in a stand mixer until smooth and slightly fluffy.
3. Add oil, vanilla, egg, and almond flavoring. Mix well, scraping down the bowl.
4. Add flour, cream of tartar, salt, and baking powder. Mix until a soft dough forms that holds its shape.
5. Divide into 8 portions and shape into thick discs. Place 2–3 inches apart on baking sheets.
6. Bake 10–12 minutes until centers are set and tops are no longer glossy. Cookies should stay pale.
7. Cool on baking sheets 10–15 minutes, then transfer to a rack to cool completely.

Frosting

1. Mix butter and powdered sugar on low until combined.
2. Add vanilla, almond flavoring, milk, and pink coloring.
3. Mix, then whip on medium speed 1–2 minutes until smooth and creamy.
4. Spread frosting over cooled cookies and swirl gently.