Beat eggs, sugar and salt in large heavy saucepan until eggs are well mixed into the sugar.
Stir in 2 cups milk.
Cook on low heat, stirring constantly but gently until mixture is thick enough to coat a metal spoon with a thick film (or use a thermometer and heat to 160⁰F degrees). It should take about 15 minutes.
Stir in remaining 2 cups milk and the vanilla.
Refrigerate until chilled (it will take several hours, and it’s best to let it chill overnight).
To serve, pour into glasses and sprinkle with cinnamon or nutmeg.