In a large bowl, whisk together eggs, sugar, and cornstarch until sugar dissolves. Set aside.
Place a medium saucepan over medium heat.
Add in milk, vanilla, and butter. Stir to combine.
Bring mixture to a simmer.
Remove the mixture from the heat.
Stir in two tablespoons of the egg mixture from the bowl. Whisk it to make sure that it is thoroughly combined.
Return the pan to the heat.
Turn the heat too low. This mixture mustn't begin to boil.
Slowly pour in the egg mixture and whisk continuously until the mixture starts to thicken. Be sure to add the egg mixture slowly. If you do it too fast, it will turn into scrambled eggs. This may take around 15 minutes. The custard should coat the back of a spoon when it is ready.
Pour the custard into dessert cups.
Refrigerate for 4 hours.
Sprinkle nutmeg and cinnamon on top before serving.
Serve cold.