Instead of cutting the oranges in slices, you can supreme them if you prefer the look of sections rather than slices. If possible, use the metric measures for the best results.
Grease a 10-inch x 2-inch circular cake pan with butter.
Finely grate the zest of the three oranges without any of the white pith. A microplane grater work well. Reserve the zest and oranges separately.
Combine brown sugar, butter, white sugar, and orange juice in a small pan. Heat, stirring frequently till butter is melted and sugar is dissolved. Raise heat and boil for 2 minutes, without stirring, until slightly thickened.
Remove caramel syrup from the heat. Stir in the zest of three oranges. Pour the caramel on the bottom of the prepared pan. Allow to set for approximately 5 minutes, until cool.
Meanwhile, slice the oranges approximately ¼ inch thick. Cut off all pith and rind. Remove the tough core from any slices that have it. Scissors work well for doing this.
After the caramel has cooled for about 5 minutes, arrange orange slices over the caramel without overlapping. Cut slices as needed to fill in the larger gaps between the full slices.
Cake and Assembly
Stir together the flour, cornmeal, baking powder and salt. Reserve.
Beat the butter in an electric mixer until lightly creamed.
Add the white sugar, then beat at high speed until light and fluffy, approximately 4 minutes.
Add eggs, one at a time, beating on medium after each addition until the egg is combined.
Mix in sour cream then vanilla and orange zest.
With the mixer on low, add the flour mixture a little at a time and mix until almost combined. Finish mixing by hand.
Spoon the batter over the orange slices in the prepared pa. Spread the batter and tap the pan to remove air bubbles.
Bake at 350°F until a cake tester comes out clean, 50-55 minutes. Cool for 10 minutes in the pan.
Using a knife, loosen the cake from the sides of the pan. Invert onto a serving dish. Cool completely.