Cream the softened butter in a large mixing bowl using an electric mixer on medium speed until light and fluffy (about 2-3 minutes).
Gradually add the powdered sugar, mixing on low speed, then add the half and half, vanilla extract, peppermint oil, and a dash of salt. Mix until smooth.
If desired, add a few drops of yellow food coloring and mix until you achieve your desired shade.
Turn the mixture onto a clean surface dusted with powdered sugar. Roll into balls or logs, or roll out to 1/4 inch thickness and cut out shapes.
Place the shaped mints onto a parchment-lined baking sheet and let them set at room temperature for 1-2 hours, or refrigerate for 30-60 minutes.
Enjoy the mints once they are set! Store leftovers in an airtight container.