Step 1

In a medium saucepan, whisk together the sugar and flour.

Step 2

, Add the milk and cook over medium heat, whisking constantly, until the mixture comes to a boil and has thickened to a pudding-like consistency, about 3 to 6 minutes.

Step 3

, Remove from the heat and transfer the mixture to the bowl of a stand mixer fitted with the beater attachment. Beat at medium-high speed for about 10 to 15 minutes, until it's below 80°F.

Step 4

, Reduce the speed to low and, with the mixer running, add the butter a few tablespoons at a time. Scrape down the sides of the bowl as needed, to make sure the butter is thoroughly incorporated.

Step 5

, Once all the butter has been mixed in, add the vanilla.

Step 6

, Increase the mixer speed to high. Beat the frosting for 4 to 6 minutes, until it’s light and fluffy.

Step 7

, If the frosting feels dense, curdled, or greasy, it’s too cold. Gently warm the mixture by setting the bowl over a pan of steaming-hot water for a few minutes (just until you see the edges begin to soften/melt), then re-whip until smooth. If the frosting feels soupy or loose, it’s too warm. Chill for 15 to 20 minutes in the refrigerator before re-whipping.

Step 8

, Use as desired to finish the cake or cupcakes of your choice; you’ll have enough for a single-layer cake or a dozen cupcakes (see “tips,” below).