In a medium bowl, whisk together egg yolks and egg. Set aside
In a small bowl, stir together cornstarch, sugar, and cardamom.
In a heavy saucepan, add cornstarch mixture to milk and whisk to combine. Bring to a simmer over medium heat, stirring constantly, just until the mixture begins to thicken.
To avoid cooking the eggs, temper them by adding ¼ cup of the hot milk mixture to the eggs in the small bowl, one tablespoon at a time. When the entire 1/4 cup of hot milk mixture has been added to the eggs, slowly pour the egg mixture to the milk mixture in the saucepan, whisking constantly. Continue stirring until the mixture boils and thickens. Remove from heat.
Whisk in butter and vanilla.
Pour into a heat-proof container and place a piece of plastic wrap directly on the surface to prevent a skin from forming. Refrigerate until chilled before using. **
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