1. Soften the butter and mix it with light corn syrup and peppermint extract in a large bowl.
2. Gradually add powdered sugar, mixing until a stiff dough forms.
3. Roll out the dough on a flat surface to about 1/4-inch thickness.
4. Use a small round cutter to cut out circles from the dough.
5. Place the cut circles on a parchment-lined baking sheet and freeze for at least 30 minutes.
6. Melt the semi-sweet chocolate in a microwave or using a double boiler, stirring until smooth.
7. Remove the peppermint patties from the freezer and dip each one in the melted chocolate, coating it completely.
8. Place the dipped patties back on the parchment-lined baking sheet.
9. If desired, drizzle extra melted chocolate over the patties for decoration.
10. Allow the chocolate coating to set completely at room temperature or in the refrigerator.
11. Store the finished peppermint patties in an airtight container in the refrigerator or freezer.