In a small saucepan, combine the cocoa powder, sugar, and pinch of salt. Stir in hot water.
Bring mixture to a boil over medium heat, stirring constantly. Simmer and stir for 2 minutes.
Stir in milk and heat until very hot, but not boiling. Remove from heat and add vanilla and peppermint extract.
Distribute evenly into 4 mugs and stir 1 Tbsp. half and half into each. Top with whipped cream, if desired.