First, whisk the eggs with the vanilla, sugar, and salt until the mixture is smooth and slightly lightened in color. Add the citrus zest and mix it in well.
Add the sour cream and baking powder, then whisk again until everything is fully combined and the mixture looks uniform.
Add the flour and mix until you get a smooth batter with no visible dry spots. Gently fold in the cooled melted butter until fully incorporated.
Pour in the poppy seeds and mix again so they are evenly distributed throughout the batter.
Transfer the batter to a prepared loaf pan lined with parchment or greased and floured. Bake at 180 °C (about 350 °F) until a toothpick inserted in the center comes out clean. Meanwhile, cook the syrup by combining all the ingredients in a small saucepan, bringing it to a boil, and letting it simmer for about three minutes.
While the loaf is still hot, soak the baked poppy seed cake with the hot syrup, pouring it slowly over the surface so it can absorb. Let the cake cool completely, then slice and serve. Enjoy!