Whisk flour, sugar, and salt in a medium saucepan until smooth and without lumps.
Place the saucepan over medium heat and slowly stir in milk and extract as the mixture heats.
Continue to stir almost continuously until the milk custard reaches a thick pudding consistency.
Remove the mixture from heat and either press plastic wrap onto the surface of the milk custard or continue to stir every few minutes while cooling to prevent a film from forming.
This mixture must be slightly cooler than room temperature to move to the next step. Allow to cool on the counter and then refrigerate until ready to use (up to three days). If leaving in the refrigerator for a lengthy amount of time, allow to warm up on the countertop until cool (not cold) for about an hour before moving to the next step.
Place slightly softened butter in the bowl of an electric mixer and whip until very light in color and fluffy.
Scrape down the sides of the bowl and continue to whip, adding the milk custard mixture to the butter by tablespoons until fully combined. Scrape down the sides of the bowl a couple of times during this process and finish with a final quick whip.