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

Gradually whisk in the whole milk until the mixture is completely smooth.

Cook over medium heat, stirring constantly, until the filling thickens and begins to bubble.

In a small bowl, slowly whisk a little of the hot chocolate mixture into the egg yolks to temper them.

Pour the tempered egg yolks back into the saucepan, whisking constantly, and cook for 2 more minutes until thick and silky.

Remove the saucepan from the heat and stir in the butter and vanilla extract until fully melted and smooth.

Pour the chocolate filling into the pre-baked pie crust and smooth the top with a spatula.

Let the pie cool for about 30 minutes, then refrigerate for at least 4 hours or until completely set.

Before serving, top with freshly whipped cream and chocolate shavings if desired.