In a large saucepan, combine the flour, sugar, and salt. Stir to combine.

Slowly whisk in the milk, adding just a little at a time, making sure it is completely incorporated before adding more. This will keep the frosting lump-free, just like when making homemade vanilla pudding. Whisk in the maple syrup.

Switch from the whisk to a silicone spatula and stir constantly over medium heat.

Continue cooking until the flour mixture has thickened and will drop off a spoon in clumps rather than pour off in a stream.

Remove from the heat and scrape into a large bowl with the spatula. Cover the top with plastic wrap that is touching the surface, and allow to cool at room temperature until it is no longer warm to the touch. You can speed this up by cooling it in 20 minute intervals in the refrigerator, stirring and repeating until it is body temperature.

In the bowl of a stand mixer fitted with the whisk attachment, beat the butter on medium-high speed until fluffy and almost white in color.

With the mixer running, add a spoonful of the maple mixture and allow it to beat in fully before adding the next. Scraping down the sides of the bowl as you go.

Stop the mixer to scrape in the last of the flour mixture and scrape down the sides and bottom of the bowl.

Add the vanilla extract and continue to whisk on high until it holds stiff peaks.

Transfer to a piping bag or spread on cakes.