Whisk butter, cream cheese, and sweetener together in a bowl with an electric mixer until creamy, about 3 minutes. Add egg and vanilla extract; whisk until smooth.
Combine coconut flour, baking powder, and salt in a bowl; whisk into butter mixture until a sticky dough is formed. Wrap dough with parchment paper into a log shape; chill in the fridge for 30 minutes.
Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Slice dough into 1/2-inch thick cookies and place 2 inches apart onto the prepared baking sheet.
Bake in the preheated oven until golden, 15 to 17 minutes.
