Melt the white chocolate in a small heavy saucepan over very low heat, stirring frequently until smooth.

Stir in the brewed coffee and vanilla extract until well combined.

Add the evaporated skim milk to the saucepan.

Increase the heat to medium and heat the mixture, stirring constantly, until it is steaming hot, but not boiling.

Pour the hot chocolate mixture into a blender.

Whiz the mixture until it becomes frothy.

Alternatively, use a hand blender to create a frothy texture directly in the saucepan.

Pour the hot white chocolate coffee into 2 cups.

Serve immediately and enjoy.