In a saucepan on medium heat, combine water, sugar and ground cardamom. Once the mixture comes to a boil, turn the heat to medium low, add in thinly sliced oranges and let simmer for 15 minutes. Set aside for later instructions.
Beat eggs, sugar and salt using a mixer. While continuing to mix everything together, slowly drizzle in the olive oil. Then, add the cardamom, orange zest, vanilla extract, and orange juice to the mixture. Sift in the baking soda, baking powder and flour, then gently fold the ingredients using a spatula.
Brush a springform pan with oil, then line the bottom and the sides of the pan with parchment paper. Arrange all the orange slices on the bottom and on the sides of the pan.
Gently pour the batter in the pan, over the orange slices. Cook on high pressure for 35 minutes then quick steam release. Let cool and serve.