Melt the butter over low heat and remove from heat (let it reach room temperature while remaining liquid).
Mix the eggs with a cup of sugar, the milk, the butter, the Cointreau, the fruit zest, 1/4 cup of orange juice and the cardamom.
Mix the liquid ingredients with the dry ones until you achieve a homogeneous mixture.
Pour the batter into a previously greased rectangular loaf pan.
Bake for 40 to 60 minutes; check if it’s done by inserting a toothpick, if it comes out completely clean, it’s ready to come out.
Take out of the oven and let it sit, then remove from the pan.
In a saucepan heat the remaining 1/4 cup orange juice and 1/4 cup sugar, once bright bubbles form in the liquid, you can pour it over the cake and spread with the help of a brush.