Combine milk, sugar, and flour in a medium saucepan over medium heat.

Stir constantly until it starts to thicken.

Combine eggs and vanilla.

Temper the egg mixture with the milk mixture.

Combine eggs and milk all while stirring constantly.

When smooth, remove from heat, let cool.

Place plastic wrap directly onto pudding to avoid a skin forming.

Chill for one hour or serve warm.