In a small saucepan, combine the milk, cream, sugar, cornstarch, and salt and whisk to combine.
Bring to a simmer and cook, whisking constantly, until the sugar is dissolved and the mixture starts to thicken, 3 to 4 minutes. Remove from the heat.
In a medium bowl, whisk the eggs until pale and frothy, about 3 minutes. Slowly add about 1/2 cup of the hot milk mixture, whisking to combine. Add the egg mixture to the hot milk mixture and return to the heat. Cook over medium-low heat, whisking constantly, for 1 minute. Bring to a simmer, stirring constantly with a heavy wooden spoon, and cook until thickened, about 2 minutes. Remove from the heat and stir in the butter and vanilla.
Transfer to a clean container and press plastic wrap against the surface to prevent a skin from forming. Refrigerate until chilled, 4 hours or overnight, before serving.
Yield: 4 cups, 4 to 6 servings