In a small saucepan over medium-low heat, whisk together the milk and vanilla until the mixture begins to simmer. Remove from heat.
In a separate large bowl, use an electric mixer to beat together the eggs, yolks, sugar, and salt for 5 minutes. The mixture will thicken and become slightly frothy.
Slowly pour the egg mixture into the saucepan with the vanilla and milk, whisking constantly to incorporate.
Return pan to medium-low heat and whisk constantly for about 5 minutes, or until temperature reaches 165 degrees.
Remove from heat and pour in the heavy cream. Stir until well combined. If desired, you can pour the mixture through a strainer to ensure there are no lumps.
If making the beverage alcoholic, stir in rum now.
Refrigerate at least 3 hours or overnight before serving.
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