Combine the cocoa, sugar and pinch of salt in a saucepan. Blend in the boiling water. Bring this mixture to an easy boil while you stir. Simmer and stir for about 2 minutes. Watch that it doesn't scorch. Stir in 3 1/2 cups of milk and heat until very hot, but do not boil.
Remove from heat and add vanilla. Divide between 4 mugs. Add the half and half to the mugs of cocoa to cool it to drinking temperature.