Pour the half and half and sugar into a wide saucepan. Warm over medium-low heat, stirring occasionally, until the sugar dissolves. Do not allow the mixture to simmer.
Sift the cocoa powder into the warm mixture a little at a time, whisking after each addition until fully incorporated and smooth.
Remove from the heat and stir in the vanilla and peppermint extracts.
Allow the creamer to cool, then transfer it to an airtight container and refrigerate. Shake well before each use.
Notes
Use a heavy-bottomed saucepan to distribute heat evenly as the creamer warms.
Taste the creamer in a cup of coffee rather than on its own to judge the sweetness and peppermint flavor.
Add a splash to homemade hot cocoa for an extra-rich chocolate peppermint drink.
Keep refrigerated in an airtight container for up to 5 days. Shake well before using, as cocoa may settle.