Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Set aside.
In a large mixing bowl or stand mixer, cream together the softened butter, oil, granulated sugar, and powdered sugar until smooth and fluffy.
Add the egg, vanilla extract, and almond extract to the butter mixture. Mix until well combined.
Gradually add the flour, salt, cream of tartar (if using), and baking powder to the wet ingredients. Mix until fully incorporated.
Using a large cookie scoop (about ¼ cup or 4 tablespoons), scoop out 9 equally sized cookie dough balls. Place them on the prepared baking sheet and flatten each to about ½ inch thickness with your hand.
Bake the cookies for 9-10 minutes. Let them cool on the baking sheet for 20 minutes before transferring them to a wire rack to cool completely. Don’t worry if they look slightly underbaked—they’ll continue baking as they cool.
While the cookies are cooling, make the pink almond sugar cookie frosting. In a large bowl or stand mixer, cream together the softened butter, powdered sugar, vanilla extract, and almond extract until well combined.
Add the cold heavy cream and beat on medium speed until the frosting is light and fluffy.
Using a toothpick, add a tiny bit of pink gel food coloring to the frosting. Mix well and adjust the color to your preference.
Generously spread the frosting over the chilled cookies. Serve immediately or chill the cookies further before serving for an extra cold treat.
Enjoy your delicious Chilled Crumbl Sugar Cookies!