In a medium bowl, beat the softened butter until smooth and fluffy.
Mix in the peppermint extract until fully combined.
Add the powdered sugar one cup at a time, mixing until a soft dough forms.
If the dough is crumbly, add ½ teaspoon milk at a time until it comes together.
If the dough is sticky, add more powdered sugar.
Pinch off pea-sized portions (about ½ teaspoon each), roll into tiny balls, and flatten gently with a fork to create the classic crosshatch pattern.
Place mints on a parchment-lined baking sheet and leave them out uncovered overnight to dry.
They will firm up on the outside but stay soft and melty inside.
Transfer to an airtight container.
Store at room temperature for up to 2 weeks, or freeze for up to 3 months.