In a medium mixing bowl, beat butter, cream cheese, and sugar with an electric mixer until light and creamy, about 2 minutes. Add vanilla and almond extracts and mix until combined. Add flour and mix again until a thick dough forms. Do not over mix. Shape dough into smooth ball and wrap in plastic. Chill in the refrigerator for an hour or two which allows for the gluten to relax and also makes it easier to roll out the dough. The dough can be made in advance then chilled or frozen.
Preheat oven to 350°F. Unwrap dough and cut into 3 or 4 pieces so it’s easier to work with. Sprinkle a little flour on a clean counter. Place a piece of dough on the floured surface and sprinkle a little more on top. Roll out dough to 1/8-inch-thickness.* Cut into shapes with cookie cutters; sprinkle with colored sugar or leave plain to frost after baking. Use a spatula to transfer cookies to baking sheets. Bake 12 to 15 minutes or until edges are lightly browned. Transfer to wire racks and cool completely before icing. (*As an alternative to rolling and cutting cookies, scoop out about a tablespoon of dough. Roll into a ball and place on the prepared baking tray. Press down with the bottom of a small measuring cup or glass to flatten. Baking time may be slightly longer, depending on how thick the cookies are.)
To make the icing, mix powdered sugar and non-dairy milk together in a small bowl. Add a tiny drop of food coloring; a little goes a long way. Spread icing on cooled cookies with a spoon or an offset spatula.