Whisk eggs, sugar and salt together in a medium-large saucepan. Set it over low heat.
Slowly whisk in 1/2 the milk. Cook gently, stirring constantly around bottom and sides with a wooden spoon until it comes to exactly 160 degrees F, about 20 minutes. Do not boil! The mixture is ready when it coats the spoon.
Remove from heat. Add vanilla, cinnamon and nutmeg along with the remaining milk. Taste and adjust spices to personal preference.
Transfer to a large ceramic or glass pitcher, serving bowl or container. Refrigerate until well chilled.
If desired, add bourbon or rum and serve with whipped cream and an additional sprinkling of nutmeg or cinnamon over the top.