Pour the pastry cream through a fine mesh strainer and into a medium saucepan. This will catch any bits of unmixed pastry cream. Stir gently and constantly while cooking over medium heat. Make sure the whisk touches the sides, corners, and bottom of the pan while stirring to avoid scorching the pastry cream.
When it starts to boil, continue cooking (and stirring constantly) for 1.5-2 minutes. During this time, the pastry cream should thicken as the flour is cooking. This stage of cooking is very important for the correct consistency. If you don’t cook it for long enough, the flour will not thicken the pastry cream and it will be too thin. If you cook it for too long, the pastry cream can curdle and become unusable.
Remove the pan from the stove top and pour the pastry cream into the interior bowl of the ice bath. This will allow the pastry cream to stop cooking immediately. Whisk the pastry cream in the bowl for about 1 minute (or until you’re unable to see steam any longer) and then add one half of the butter. Stir until the butter is completely incorporated before adding the second half of butter. Stir to combine.