In a medium saucepan, heat milk and heavy cream on medium heat just to a boil. Remove from heat and gradually pour the hot milk mixture into the egg mixture while simultaneously whisking constantly until smooth (this will prevent the eggs from being cooked by the heat). Transfer mixture back into saucepan. Cook over medium-low heat, whisking constantly and vigorously so that the eggs won’t curdle, until mixture thickens and bubbles burst on the surface. Remove from heat and whisk in butter, vanilla, and salt. Strain through a fine-mesh strainer set over a bowl. Cover with plastic wrap directly on top of the filling to prevent a skin from forming. Allow to cool to room temperature, then refrigerate until chilled.