Prepare the Peppermint Filling: In a medium-sized mixing bowl, combine 1 1/2 cups powdered sugar, 1/4 cup heavy cream, and 1 teaspoon peppermint extract. Mix well until smooth and creamy. The mixture should hold together well, so adjust the heavy cream to achieve the desired consistency.
Shape the Filling: Using your hands, form small discs of the peppermint mixture, approximately 1 inch in diameter and 1/4 inch thick. Place these discs on a parchment-lined baking sheet. Make sure they are evenly spaced to allow for easy coating later. Chill them in the refrigerator for about 30 minutes, or until they firm up.
Melt the Chocolate: While the peppermint centers are chilling, melt the 1 1/2 cups dark chocolate chips and 1/4 cup unsweetened cocoa powder in a double boiler or microwave. If using a microwave, heat in 30-second intervals, stirring until smooth with no lumps. Avoid overheating the chocolate to prevent it from seizing.
Coat the Centers: Once the peppermint centers are firm, use a fork or toothpick to dip each one into the melted chocolate. Ensure an even coating, and allow excess chocolate to drip off before placing them back on the parchment paper.
Chill to Set: After coating the peppermint patties in chocolate, return them to the refrigerator to set completely. This should take about 30 minutes.