Step 1

MAKE CANDIED ORANGES: Combine the water and sugar together in a medium saucepan; bring to a boil over high heat. When boiling, lower the heat to medium-low, gently add in the orange slices, making sure they are mostly covered in the syrup, and simmer for 15 minutes, stir and move the slices around often so that all of them soak evenly. Once cooked, turn off the heat, remove from heat and allow them to cool for several minutes until you can handle the slices with needle-nose tongs or with your fingertips. Prep while the oranges are soaking in syrup.

Step 2

PREP: Position a rack in the center of the oven and preheat the oven to 350ºF. Spray a 9-inch springform pan with cooking spray on the bottom, up the sides, and line the pan with a sheet of parchment paper. Zest the remaining two oranges using a zester. Remove all of the white pith from the orange using a paring knife and cut the oranges into small pieces (remove seeds and any additional pith to keep the cake from being too bitter.) Place the cut-up orange segments and zest in a food processor and pulse the oranges until they break down into an applesauce-like consistency. Arrange the soaked orange slices in the springform pan in a scaled overlapping pattern; set aside. Do not discard the syrup.

Step 3

MIX: In the bowl of a stand mixer, whip together the eggs and granulated sugar until it's pale and fluffy, about 5 minutes. Slowly stream in the olive oil with the mixer running. Add the flour, kosher salt, nutmeg, and baking powder and combine on the ‘stir’ setting. Add the yogurt as the mixer is running and continue to mix until incorporated. Then, add the vanilla, pulsed orange mixture, and stir until the batter is combined.

Step 4