Preheat the oven to 170 degrees Celsius. Line a springform cake tin (or any circular cake pan) with baking paper or grease the sides using non-stick spray or even just butter.
In a large mixing bowl, soften butter, then mix it with sugar. Beat this together until pale and creamy. Beat in orange zest and vanilla extract. Add eggs, one after the other, beating well after each addition. Scrape down the sides of the bowl occasionally. Add crushed cardamom, cinnamon, baking powder, and salt. Gently mix in flour, semolina, and sour cream or greek yogurt. The batter must be quite thick. Pour the batter into the cake tin. Spread evenly and smoothen the top. Check that the oven has reached the correct temperature, then place the tin on the middle rack of the oven. Bake for 50 to 60 minutes. The cake is ready when golden-brown on top and a skewer into the centre comes out clean. While it is baking, prepare the syrup. For this, juice the orange and lime into a saucepan. Add sugar, pods of cardamom, and liqueur. Heat the syrup gently over low heat, stirring until the sugar has dissolved. Let the syrup simmer for 5 minutes over low heat. Strain the syrup into a bowl and set aside.
When the cake is removed from the oven, poke about 50 holes all over the cake while it's still warm. Pour the syrup evenly over the cake. It looks like a lot of syrup, but the cake will soak it all up. Let the cake cool in the tin before releasing the clip.