Put the milk and vanilla in a saucepan and bring to a simmer over medium heat.
In a bowl, whip together the sugar, flour, and egg yolks with a hand mixer. Ladle the cup of the milk-vanilla mixture into the bowl and beat to temper the yolks.
Add the yolk mixture to the pot and beat over medium heat with the hand mixer until thick and creamy, about 1 minute. As you are beating, move the pot on and off the flame so that you don’t scramble the eggs.
Remove the pot from the heat, add the butter, and whip for 2 minutes to thicken the cream. Transfer to a bowl. Let cool, cover with plastic wrap, and refrigerate at least 6 hours.
Will keep for up to 1 week.