Preheat the oven to 350°F and prepare a baking sheet with parchment paper. Set it aside.

In a large bowl or stand mixer, cream together the butter, oil, granulated sugar, and powdered sugar until smooth.

Add the egg, vanilla extract, and almond extract. Mix until everything is well blended.

Combine the flour, salt, cream of tartar, and baking powder in another bowl, then gradually add to the wet mixture until fully incorporated.

Using a large cookie scoop (about 1/4 cup), scoop out 9 cookie balls, place them on the baking sheet, and flatten each to about 1/2 inch thick.

Bake for 9-10 minutes. Allow the cookies to cool on the baking sheet for 20 minutes before transferring them to a wire rack to cool completely.

For the frosting, in a large bowl or stand mixer with a paddle attachment, cream the butter, powdered sugar, vanilla extract, and almond extract until smooth.

Add the heavy cream and beat on medium speed until the mixture is light and fluffy.

Use a toothpick to add a tiny bit of pink gel food coloring, mix, and adjust the color as desired.

Generously spread the frosting on the chilled cookies. Serve immediately or chill further before serving.