In a saucepan, heat the milk over medium heat until it just starts to simmer. Stir it occasionally to prevent scorching.

In a separate bowl, whisk together the granulated sugar, flour, and egg yolks until smooth and well combined.

Slowly pour the hot milk into the egg mixture while whisking continuously to temper the eggs and prevent them from curdling.

Return the combined mixture to the saucepan. Cook over medium heat, stirring constantly until the mixture thickens and begins to bubble.

Once thickened, remove it from the heat, then stir in the unsalted butter and vanilla extract until fully melted and combined.

Transfer the pastry cream to a bowl, cover with plastic wrap, and let it cool completely before using.