Preheat oven to 350° and set a rack just below the middle position. Grease and flour two standard round cake pans.
In a large bowl, sift together flour, sugar, baking powder, and salt. Add shortening (or butter), then milk and vanilla. Beat 2 minutes. Add eggs and beat 2 minutes.
Bake in two pans until layers are golden-brown and a cake tester comes out clean, 25 to 30 minutes. (This is a good time to make the icing; see the accompanying recipe.) Remove from oven. Let layers sit in pans 5 minutes; then remove gently and let cool 15 minutes on wire racks.
When cool, frost the top of one layer with icing; then stack the second layer on top. Set a cooling rack into a rimmed baking sheet; then place cake atop rack. Pour remaining icing over cake, letting it drip down sides and into pan. Serve.
Esther Foskett's Vanilla Icing
This old-fashioned icing takes just minutes to make. The recipe yields just enough to cover the cake. If you like lots of icing, or want to decorate it, you can easily double the quantities.
Using a hand-held or standing mixer, blend sugar and butter. Add vanilla and blend until smooth. Add milk 1 tablespoon at a time, blending as you go; add only as much as you need to get the desired texture. If you'll be piping the icing as decoration, add less milk. If you plan to simply frost the cake, use a bit more.
Not only is this cake so delicious that our tasters gobbled it up in a single sitting, but it's also incredibly easy to make. If you've always been intimidated by scratch cakes, start with this one. You'll never go back to boxed mixes again.