Preheat the oven to 350°F. Line and grease the bottom of a springform pan. Place 1 cup of water or coffee to boil (or use a kettle)
Zest the four oranges. Put the zest in a bowl and set the oranges aside. Add the sugar into the bowl and massage together with your fingers for about 1 minutes, until the sugar is orange and aromatic. Set aside.
Of the four zested oranges, slice one orange into one-inch pieces. Cut off the extra peel left, so that the orange rounds do not have peel left. Place the orange slices onto the bottom of the springform pan. If there are empty nooks and you want a more full look, feel free to slice another ½ orange the same way to fill up the pan.
Juice the remaining 2½ or 3 oranges and set aside.
Place a fine mesh strainer over a large bowl. Add the flour, cocoa powder, baking soda, baking powder, salt, and espresso powder (if using) into the strainer and sift until the dry mixture is all in the bowl. This helps getting the clumps out of the flour and cocoa powder and helps combine.
To the large bowl with dry ingredients, add in the orange-sugar mixture, olive oil, lemon juice, orange juice, and vanilla extract. Using a spatula, mix together the wet and dry ingredients until a smooth batter is formed.
Pour the batter over the sliced oranges in the springform pan. Bake for 35-45 minutes. Once done, let cool, then flip upside down. Enjoy warm or cold!