Preheat the oven to 350°F. Lightly grease a 9-inch by 2-inch round cake pan. Line the bottom of the pan with waxed paper and lightly grease the bowl (to ensure the perfect fit, place the cake pan on a piece of wax paper and trace an outline of the bottom with a marker and then cut out the circle). I greased the pan with unsalted butter (don't forget to do the sides)
In a large bowl, sift together the flour, sugar, baking powder, and salt.
In a medium bowl, whisk together the egg yolks, oil, water, grapefruit juice, and lemon zest until smooth. Whisk in the flour mixture.
Beat the egg whites and the cream of tartar in a stand mixer in a medium bowl until stiff peaks start to form. With a rubber spatula, gently fold the egg whites into the yolk mixture, until just blended. Pour into the prepared pan (the video link has a great example of this technique).
Bake for 25 to 30 minutes, or until the cake springs back when touched lightly in the center. Invert the cake, still in the pan, and cool on a wire rack (if the cake slides out of the pan, that's fine too - it didn't seem to make any difference when this happened to me). If making this recipe over 2 days, run a spatula or a table knife around the edge of the cake. Carefully remove the cake from the pan and place the cooled cake on a plate and store in the refrigerator overnight (this makes it easier to cut the layers).
With a serrated knife, remove the dome to make an even top. Then cut the cake horizontally into the desired number of layers (cut it in half once to have 2 layers or or cut it evenly twice for a 4 layer cake). There is a how-to video link in the notes below.
Spread the grapefruit puree onto the top of the bottom layer. Wait a few minutes to ensure the puree completely soaks into the cake. `Next, spread the Cream Cheese Frosting on top. Place the next layer on top of the frosting and repeat this step (if your cake will have 4 layers, repeat twice).
Frost the top and sides of the cake. Drizzle some of the puree on top (if you have leftover grapefruit sections, you can use these as garnish.)