Preheat the oven to 350°F. Lightly grease a 9-by-2-inch round cake pan and line with a parchment circle. Lightly grease the parchment and set the pan aside.
Start by zesting and then segmenting the grapefruits. Reserve the zest for later in a small bowl covered with a damp piece of paper towel to keep it from drying out. Cut off the top of bottom of a grapefruit and stand it up on one of the cut edges on a cutting board. Use your knife to carefully cut off all of the rind moving from top to bottom in strips, keeping with the natural curve of the fruit. Carefully cut in between each membrane to remove grapefruit segments (supremes).
Put removed segments in a strainer set over a bowl to collect juices. When all segments are removed, and only a juicy mass of membrane is left, squeeze the remaining juice from the membranes into the same bowl over which the grapefruit is draining. This fresh juice will be strained and used in the cake and frosting later. Repeat with the remaining grapefruit.
To make the cake, sift together flour, sugar, baking powder, and salt into mixing bowl. Make a well in center of dry ingredients.
In a separate bowl add the water, oil, egg yolks, grapefruit juice, and zest. Beat until smooth. Then add the wet ingredients to the well in the center of the dry ingredients and beat until just mixed. Do not over beat.
In the bowl of an electric mixer fitted with the whisk attachment, beat the egg whites and cream of tartar until whites are stiff but not dry.
Gradually fold the egg whites into the cake batter (about ½ at a time), folding gently with a rubber spatula until just blended, but do not over mix.
Pour the batter into the prepared pan and bake for 20 to 25 minutes, or until cake springs back when lightly touched with a finger and a toothpick inserted into the center comes out clean. Invert pan on a wire rack until cool (If the pan slides off by itself, that’s fine, but if not, just leave the pan on until the cake is cool).
If still in the pan, run a spatula around the edge of cake. Carefully remove from pan and carefully peel off the parchment paper circle from the bottom of the cake. With a serrated knife, gently cut the cake in half to form two layers.
In the bowl of an electric mixer fitted with the paddle attachment, beat the cream cheese on high speed until smooth and fluffy. Add the grapefruit juice and zest. Gradually blend in confectioners’ sugar and beat until well blended. Add food coloring, if desired.
Invert the cake so the top of the cake is on the bottom and the smoother bottom is now the top. Spread about ¼ of the cream cheese frosting on top of the first half of the cake to make the filling. Frost the cut side of the other cake half with another ¼ of the frosting.
Save the 8 prettiest grapefruit segments for topping the cake, and roughly chop the remaining grapefruit. Distribute the chopped grapefruit over the first frosted cake half.
Cover the bottom half (with the grapefruit on it) with the other half frosted-side down. This makes it like a sandwich with frosting on both sides surrounding the grapefruit. The flat, browned bottom of the cake should now be the top.
Frost the top and sides of the cake with the remaining frosting. Garnish with the remaining grapefruit sections and serve.