In a stand mixer, cream together the softened cream cheese and butter on medium-high speed until perfectly smooth and emulsified.
Add the pure peppermint extract and mix on low until incorporated.
Gradually add the sifted powdered sugar one cup at a time. Beat on medium speed until the mixture forms a stiff, smooth dough.
Transfer the mixture to a piping bag and pipe quarter-sized buttons onto parchment-lined baking sheets.
Place the baking sheets in the freezer for at least 2 hours, or until the buttons are completely solid.
Melt the dark chocolate and coconut oil together in the microwave using 30-second increments, stirring until smooth and glossy. Let cool for 5 minutes.
Working in batches, dip the frozen cream cheese buttons into the melted chocolate, tapping off the excess. Place back on the parchment paper to set.
Store in an airtight container in the refrigerator until ready to serve.
