Whisk together flour and water in a medium saucepan and cook over medium heat, stirring constantly, until the mixture becomes a thick paste. Cover and set aside to cool to room temperature (2 hours).
Using a stand mixer fitted with the whisk attachment, beat butter, sugar and vanilla on high speed, scraping bowl with a rubber spatula occasionally, until lightened. Add the cooled flour mixture and beat on high until very fluffy. It should have a light and silky texture with no remaining sugar crystals.
If frosted with Original Red Velvet Frosting, the cake doesn’t need to be chilled but should be eaten within a couple of days.