In a large mixing bowl, combine the eggs, sugar, and cornstarch. Use a whisk to beat the mixture until it's completely smooth and homogenous, about 2 minutes.

In a medium saucepan, pour in the whole milk, vanilla extract, and add the butter. Place the saucepan over medium heat and warm the mixture until it starts to simmer, which should take around 5–7 minutes.

Once the milk mixture is simmering, remove it from the heat. Gradually drizzle the hot milk into the egg mixture while whisking continuously to prevent the eggs from scrambling.

Return the combined mixture to the saucepan over low heat. Stir constantly for about 10–15 minutes until the custard thickens enough to coat the back of a spoon.

Once thickened, pour the vanilla custard into individual serving cups or a larger bowl. Allow it to cool to room temperature for about 30 minutes.

Cover the vanilla custard with plastic wrap, pressing it directly onto the surface to prevent a skin from forming. Refrigerate for at least 4 hours.