Preheat oven to 350°F. Line two large cookie sheets with parchment paper.
In a large mixing bowl with a paddle attachment, cream the butter, cream cheese, and sugar until light and fluffy. Add in egg and beat until combined.
In a separate bowl, combine flour, baking soda, salt, and spices. Slowly add the dry ingredients into the wet, mixing on low speed until just combined.
Roll out 1/2 ounce balls of dough (about the size of a large marble) and press slightly into the cookie sheet, forming a flattened disk. Bake for roughly 8 minutes, so that the cookies are still soft to the touch. Allow to cool completely before frosting.
To make the frosting, whip the butter, cream cheese, sugar, and chai concentrate until light and fluffy. Place into a small piping bag and pip out dollops of frosting over the undersides of half of the cookies. Top with other half of cookies to make cookie sandwiches!