Wash the oranges anc cut into thin slices. Place the water and sugar into a medium sized pot over medium high heat and add the orange slices. Boil the oranges for 10 minutes to infuse the sugar into a slices. Remove from the water and place on a wire rack to dry for 1 hour. Place the orange slices on to parchment or a silicon mat and place them into an oven at 250F for 2 hours, flipping haplf way through. Allow to completely cool before placing them on the cake.
For the Cake
Preheat oven to 350F. Grease two 8 or 9-inch round cake pans. Prepare the pans with parchment paper; grease the paper. Set pans aside.
In a large mixing bowl beat the eggs and sugar with an electric mixer about 5 minutes or until pale and thick ribbons form.
In another large bowl whisk together the flour, baking soda, baking powder, and salt. In a medium bowl combine the olive oil, orange peel, orange juice, and buttermilk.
Beat the vanilla into beaten egg mixture on low speed. With mixer on low speed, add the dry and wet ingredients in three additions, starting with dry and ending with wet. After the last addition, turn mixer off and whisk until combined. Divide batter among prepared pans, filling each half full. Use baking strips around the pans to ensure that they bake up level.
Bake for 25 to 30 minutes or until a toothpick inserted near the centers comes out clean and cakes are golden and pull away from sides. Remove and cool in pans on wire racks for 10 minutes. Remove from pans and cool completely on a wire rack.
For the Frosting
In a large bowl beat cream, sugar, and peel with an electric mixer or large whisk until soft peaks form. Cover and chill up to 4 hours ahead. Whisk before serving.
Place one cake layer on a serving plate. Spread top of cake with ¼ of the whipped cream. Place another cake layer on top. Spread with another ¼ of the whipped cream. Continue with all four layers frosting the sides. Scrape off as much or as little of the whipped cream from the sides if you want the cake to show through.
Top with dried orange slices and serve.
For the orange glaze
Reserve the simple syrup from boiling the oranges. Add a few tablespoons of powdered sugar and some orange food coloring. Drizzle over cake.