In a heavy bottom saucepan, combine heavy cream, milk, and vanilla extract. Cook over medium low heat until mixture is steaming (but not boiling), around 2–3 minutes.
Meanwhile, whisk sugar, pistachio paste, and egg yolks together in a medium sized mixing bowl. Once the milk and cream mixture is steaming, stream the hot mixture over the eggs while quickly whisking.
Whisk the egg mixture back into the saucepan with milk and cream. Continue to cook on low heat, stirring constantly for about 5 minutes, until the crème anglaise thickens and can coat the back of a wooden spoon.
Strain with a fine mesh strainer, and immediately place a piece of plastic wrap directly on the surface to prevent a skin from forming, then allow to cool.
Serve alongside your favorite dishes such as donuts, cakes, pastries, fruits, soufflés, french toast, waffles, and more.