Whisk 1/2 cup of the whole milk with the cornstarch in a saucepan until completely smooth and free of lumps.
Whisk in the remaining whole milk, heavy cream, sweetened condensed milk, nutmeg, cinnamon, and salt.
Cook over medium heat, whisking frequently, until the eggnog is steaming and slightly thickened, about 6 to 8 minutes. Do not allow it to boil vigorously.
Remove from the heat and stir in the vanilla extract and optional rum extract. Cool for 20 minutes, stirring occasionally to prevent a skin from forming.
Refrigerate for at least 4 hours until thoroughly chilled. Whisk well before serving, adding a small splash of milk if a thinner consistency is preferred.
