Ensure butter is softened at room temperature. It should be soft enough that you can easily press your finger into it, but not so soft that it appears shiny and greasy.

Combine powdered sugar and flour in a 1 quart saucepan and whisk to blend evenly and break up any lumps. Slowly pour in milk while whisking then place the pan over medium-low heat and continue whisking until sugar dissolves and mixture thickens slightly. Do not boil. It will get quite hot and you will see some small bubbles forming around the edges of the pan as it almost simmers and that is your sign to turn off the heat. It will take about 5 minutes. It should be thick enough that you are able to draw a defined line across the mixture coated over the back of a spoon with your finger. Pour it out into a clean bowl and refrigerate until cool. It should not be cold, but it should not be hot. It should be at room temperature.

Place butter in the bowl of an electric stand mixer and whip for 10 minutes on medium-high speed until very pale and creamy, almost white. Stop several times during mixing to scrape down the sides and around the bottom of the bowl so that all of the butter is evenly incorporated.

Very slowly drizzle the cooled sugar mixture into the whipped butter in 5 or 6 additions while whipping on medium speed. I like to pour it in near the side of the bowl so it hits the bottom of the bowl and incorporates thoroughly instead of hitting the whip attachment and spraying everywhere. Stop to scrape down the sides of the bowl periodically. After about 5 minutes, it should appear very thick, fluffy, pale and creamy. You can use it immediately or cover the bowl if using within an hour or two. You can also add meringue powder at this stage after you mix in all of the sugar syrup if desired for increased stability.