This was (and is) my favorite frosting that my maternal grandmother, Mary, made every year for my birthday until her death in 1986. I have found similar recipes called "poor man's frosting". I came across her original hand-written recipe in 2015. It was always put on a devil's food cake. I used whole milk as the additional milk fat helps incorporate the flour with less chance of lumps.
Whisk flour, milk and sugar over medium heat. Bring to a boil, stirring constantly, until thickened. Continue cooking 2-3 minutes. Remove from heat and transfer to a mixing bowl and allow to cool completely.
Add shortening to cooled mixture, beating to incorporate. Add powdered sugar and vanilla. Beat until light and fluffy, scraping bowl as needed.