Heat the coffee in a small saucepan over medium-high heat until it comes to a boil. Cook at a low boil until it is reduced to 1/4 cup, about 20 minutes. Set aside to cool.
Heat the cream and milk in a 2-quart saucepan over a medium heat. Meanwhile, in a medium-sized mixing bowl, combine the sugar and the egg yolks and beat until well-blended and pale yellow in color. Once the cream and milk come to a simmer, remove from the heat and pour about 1/2 cup of the cream and milk mixture over the eggs and whisk to blend. Return the saucepan to the stove, and add the egg-cream mixture. Cook, stirring well with a wooden spoon, being sure to reach into the corners of the pan. Continue to cook, stirring, until the anglaise begins to thicken and coats the back of the spoon, about 5 minutes. Once thickened, remove from the heat and strain into a clean bowl using a fine mesh sieve. Add the vanilla and the reduced coffee to the anglaise and stir to combine. Serve warm, at room temperature or chilled, with the beignets.
Yield: 1 1/2 cups