Heat the oven to 350? F. Ignore the ingredients list and instructions on the back of the Vanilla Cake Mix bag.
Drain the orange segments into a strainer set over a bowl. Reserve 5 segments to for which to decorate the top of the cake. Measure out the juice. You need a half a cup. If you have less then a half cup add water to make it a 1/2 cup.
Combine the orange segments, half a cup of juice, gluten-free flour mix, vanilla, mayonnaise and the eggs in the bowl of a mixer. Using the beaters or the whisk combine the ingredients till smooth. For me it wasn't as runny as normal cake batter but it wasn't stiff either.
Spilt the batter between two 8 inch cake rounds that have been greased and have a parchment round on the bottom. Bake for 35 minutes or until a tester or toothpick comes out clean. Or, if you will, the cake is firm to the touch when you gently push down on the middle. Remove from the oven. Cool on a rack until completely cool. You could stop here and once the cakes are cool carefully wrap them and let the sit till the next day to ice them.
To make the frosting put all the frosting ingredients into a mixing bowl and whisk with the whisk attachment until the cream forms stiff peaks being careful not to turn the frosting into a flavored butter.
Place one of the layers of cake onto a cake stand and ice the top. Place the other layer onto the top of the icing and ice the rest of the cake. Fan out the 5 segments of orange to make a pinwheel in the center of the cake. Refrigerate or serve.