Combine the half-and-half, whole milk, allspice and sugar in a large saucepan and heat until steaming.
Whisk the egg yolks in a small bowl and ladle some of the hot mixture into the bowl while whisking constantly. Then whisk the tempered egg mixture back into the remaining hot liquid. Stir until mixture coats the back of a wooden spoon, then place immediately into an ice water bath. Once it has cooled down to room temperature, add liquors and chill. Serve very cold.