Whisk eggs, sugar, brown sugar, and vanilla until fluffy. Mash the bananas and melt the butter. Mix flour, baking powder, salt, cardamom, and cinnamon and sift it into the egg mixture. Add butter, mashed bananas, and sour cream and fold everything together well. Pour the batter into a greased and sugared loaf pan and bake the cake for about 45-55 minutes at 180 degrees Celsius (356 degrees Fahrenheit) on the second-lowest rack. Turn the cake out and let it cool on a rack before serving! Enjoy!!