Beat butter, oil, and sugar in a large bowl with an electric hand mixer until smooth and creamy. Beat in milk, vanilla, almond extract, and eggs.
Combine flour, salt, baking soda, and cream of tartar in a separate bowl. Stir into the wet ingredients till thoroughly combined.
Roll dough into 1 1/4" balls. Place the cookie dough balls at least 2 inches apart on a lightly greased or silpat-lined cookie sheet.
Pour the 1/4 cup sugar into a shallow dish. Dip the bottom of a glass in the sugar and flatten cookies till they are between 1/4" and 1/2" thick.
Bake at 350° for 8-10 minutes. Let the cookies sit on the pan for 3-5 minutes, then remove to a cooling rack and cool completely.
For frosting: Beat cream cheese and butter till smooth. Beat in powdered sugar, vanilla, almond extract, and salt. Add milk as needed to make a spreadable consistency. If desired, add food coloring to make a pink frosting.
Spread the frosting on top of the cooled cookies.