Bright Citrusy Italian Orange Cake (Sicilian Whole Orange Cake)

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• ¾ cup water
  Ingredient note

  Source: ¾ cup water
• ¾ cup + 1 ¼ cup granulated sugar
  Ingredient note

  Source: ¾ cup granulated sugar; Source: 1 ¼ cup granulated sugar
• 10 ounce oranges (~2 oranges; sliced into ⅛- ¼ inch slices)
  Ingredient note

  Source: 10 ounce oranges (~2 oranges; sliced into ⅛- ¼ inch slices)
• 2 each medium oranges
  Ingredient note

  Source: 2 medium oranges
• 3 each large eggs (room temperature)
  Ingredient note

  Source: 3 large eggs (room temperature)
• 1 ¾ cup all-purpose flour
  Ingredient note

  Source: 1 ¾ cup all-purpose flour
• ½ teaspoon kosher salt
  Ingredient note

  Source: ½ teaspoon kosher salt
• 1/8 teaspoon ground nutmeg (optional)
  Ingredient note

  Source: 1/8 teaspoon ground nutmeg (optional)
• 1 tablespoon baking powder
  Ingredient note

  Source: 1 tablespoon baking powder
• 5 tablespoons olive oil
  Ingredient note

  Source: 5 tablespoons olive oil
• 5 tablespoons plain yogurt (room temperature)
  Ingredient note

  Source: 5 tablespoons plain yogurt (room temperature)
• 2 teaspoons vanilla extract
  Ingredient note

  Source: 2 teaspoons vanilla extract

1. 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.
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.
3. MIX: In the bowl of a stand mixer, whip together the eggs and granulated sugar until it 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.
4. BAKE: Pour the cake batter into the prepared baking pan. Smooth out the top of the cake and bake the cake for 47-57 minutes or until a toothpick comes out clean. Allow the cake to cool in the pan for at least 30 minutes before attempting to remove it. Run a knife along the inner rim of the springform pan to help release the cake. Release the spring and remove the rim. At this point, allow the cake to cool completely before attempting to level it with a serrated knife. Once cooled, place a plate over the cake, gently flip, and peel back the parchment paper. At this point, you can brush any remaining orange syrup on the cake to give it a beautiful sheen. Slice and serve!