In a saucepan, heat the milk with vanilla (pod + seeds, paste, or extract) until it just begins to simmer. Remove from heat and let the flavor infuse.

Prepare the egg mixture

In a mixing bowl, whisk together the egg yolks, sugar, cornstarch, and salt until smooth and pale. Add vanilla here if using extract or paste.

Temper the eggs

Slowly pour the hot milk into the egg mixture in a thin stream, whisking constantly to avoid scrambling.

Cook the pastry cream

Return the tempered mixture to the saucepan over medium heat. Whisk continuously until the cream thickens and begins to bubble, about 1–2 minutes.

Finish cooking

Reduce the heat slightly and cook for 1–2 more minutes, whisking well to fully cook the cornstarch.

Add the butter

Remove from heat and stir in the butter until smooth and glossy.

Strain and cover

Strain through a fine sieve into a clean bowl if desired. Cover with plastic wrap pressed directly onto the surface.

Cool and chill

Let cool to room temperature, then refrigerate until set. Whisk before using.