In a medium saucepan, combine the sugar, water, butter, and vanilla extract.

In a medium saucepan, whisk together the sugar, flour, and salt.

Gradually add the milk, whisking constantly to combine.

Cook over medium heat, stirring constantly, until the mixture thickens and comes to a gentle boil.

In a small bowl, temper the egg yolks by slowly whisking in a small amount of the hot mixture.

Gradually add the tempered egg yolks back into the saucepan, whisking constantly.

Return the saucepan to the heat and cook for another 1-2 minutes, until the sauce is thick and creamy.

Remove from heat and stir in the butter and vanilla extract until fully combined.

Allow the sauce to cool slightly before serving. It can be served warm or chilled.

In a medium saucepan, heat the milk over medium heat until it is hot but not boiling. Remove from heat.

In a separate bowl, whisk together the egg yolks, sugar, cornstarch, and salt until well combined and slightly thickened.

Slowly pour the hot milk into the egg mixture, whisking constantly to prevent the eggs from curdling.

Pour the mixture back into the saucepan and cook over medium-low heat, stirring constantly, until the mixture thickens and coats the back of a spoon (about 5-7 minutes). Do not let it boil.

Remove the saucepan from the heat and stir in the vanilla extract.

Transfer the custard sauce to a bowl and cover with plastic wrap, pressing it directly onto the surface of the custard to prevent a skin from forming. Let it cool to room temperature, then refrigerate until chilled.