Slice 3 oranges thinly with the peel. Pour the water, 1 1/4 cups sugar, and 5 crushed cardamom seeds into a large pot. When the mixture is boiling, add the orange slices, reduce the heat to medium, and simmer for 15 minutes to candy the oranges.

Beat the eggs with 1 cup sugar and the salt until the mixture becomes frothy. Add the olive oil and mix again. Add the vanilla extract, orange zest, orange juice, baking powder, and the remaining 10 crushed cardamom seeds. Mix again.

Add the flour and gently mix with a spatula.

Preheat the oven to 350°F (180°C).

Pour a little olive oil into a pan and spread it around using a brush. Place the candied orange slices on the bottom and sides of the pan. Pour the cake batter on top.

Bake for about 50 minutes.

Let the cake cool before removing it from the pan. Use the remaining syrup from candying the orange slices on the cake; you can apply it with a brush. The cake will be even more moist.