Preheat the oven to 160° C fan.
Melt the butter & set aside to cool down.
Line the baking tin with baking parchment; add some oil to the bottom & the sides to allow the baking parchment to stick appropriately.
Grate the lemon zest & squeeze the lemon juice.
Whisk the eggs & the sugar with your handheld electric mixer (beaters) until foamy.
Add the molten butter & whisk until well incorporated. It's rather liquid.
Mix the flour, the baking powder & the salt. Add the liquid mess & whisk until incorporated.
Add the cream & whisk ...
Fold in the lemon zest with a spoon.
Pour the mess into the prepared baking tin & bake for about 30 min.
Make the famous test with the wooden pin ... If necessary add 5 - 10 min to the oven session.
For the icing mix the lemon juice & the icing sugar with a spoon until creamy w/o any tiny lumps of sugar.
Distribute the lemon icing all over the cake as soon as the cake is out of the oven & chills on the cooling rack. If you like you may pierce some little holes in the cake with the wooden pin to enhance the soaking.
Let the cake rest until at room temperature before removing the baking tin and the baking parchment.