Whisk egg yolks, cream, sugar, brandy-based orange liqueur, and vanilla extract in a small saucepan until smooth.
Place saucepan over medium-low heat and cook, stirring constantly with a rubber spatula scraping the bottom, until the mixture is hot and thickens slightly, and a thermometer reaches 180 degrees F (82 degrees C), 8 to 10 minutes.
Remove from heat, strain to remove any over-cooked particles of egg, and allow cool.
For added orange flavor, add some freshly grated orange zest to the cooled creme Anglaise.
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