I always start by preheating my oven to 360°F (180°C) so it's fully heated by the time my batter is ready. Line your 7-8 inch cake pan with parchment paper and grease it generously. This little step makes removing the cake so much easier later.
Using an electric mixer, beat the eggs and sugar together on high speed for about 5 minutes. You're looking for a thick, pale, and fluffy mixture. This step builds the airy texture the cake is known for, so don't rush it.
Gradually mix in the olive oil, vanilla extract, orange zest, and sour cream. Beat on a lower speed just until everything is combined. Going slow here keeps the batter smooth and prevents it from deflating.
In a separate bowl, whisk together the flour, baking powder, salt, and ground cardamom. Mixing the dry ingredients first ensures the cardamom and baking powder are evenly distributed through the batter.
Using a rubber spatula, gradually fold the dry mixture into the egg mixture, alternating with the blood orange juice. Mix just until no flour lumps remain. Overmixing at this stage can make the cake dense instead of light.
Pour the batter into your prepared pan and bake for about 40 minutes. Check for doneness with a toothpick inserted in the center; it should come out clean or with just a few crumbs. Baking time can vary slightly depending on your pan size.
Let the cake cool in the pan for 20 minutes before transferring it to a serving plate. Once it's cooled, whisk the powdered sugar and blood orange juice together little by little until smooth, then pour it generously over the top.