Prepare an Ice Bath and Strainer: Fill a large bowl with ice cubes and cold water, about halfway. Set a medium bowl inside it and place a fine mesh strainer over the medium bowl. You’ll strain and chill the finished sauce here.
Heat the Milk and Cream: In a medium saucepan, combine the milk, heavy cream, and vanilla bean paste. Heat over medium heat, stirring frequently, until it just begins to simmer (about 190°F on an instant-read thermometer).
Whisk the Egg Yolks and Sugar: While the milk mixture heats, whisk the egg yolks and sugar together in a large bowl until the mixture is thick, pale, and slightly fluffy—about 2 to 4 minutes. You can do this by hand or with an electric mixer. Temper the egg mixture by slowly pouring the hot milk mixture into the yolk mixture, whisking constantly to prevent curdling.
Cook the Custard: Return the mixture to the saucepan and place over medium-low heat. Cook, stirring constantly with a wooden spoon or heatproof spatula, until the custard thickens and reaches 180°F to 185°F. It should coat the back of the spoon.
Strain and Cool: Immediately pour the custard through the prepared strainer into the bowl set in the ice bath. Stir gently, then place a piece of plastic wrap directly on the surface of the sauce to prevent a skin from forming.
Cool: Cool to room temperature in the ice bath, then refrigerate until ready to serve. The sauce will keep for up to 3 days in the fridge. Drizzle over cakes, desserts, bread pudding, or fresh fruit. Enjoy!