Mix the eggs, sugar and vanilla. Gradually add the flour and baking powder, and a pinch of salt and continue mixing. Melt the butter and add it to the mixture. You can add poppy seeds if you like.
Finely grate the skin of the lemon (do not grate the white skin as it is bitter), and add the zest to your preparation. Add the juice of half a lemon.
Preheat your oven to 180 ° C (Th 6).
Line a cake pan with baking paper and pour your preparation. Bake for 40 minutes at 180°C. Check with the tip of a knife that your cake is baked. Once cooked, let it cool on a rack.
Once the cake has cooled, prepare the frosting: mix the icing sugar with 2 tablespoons of lemon juice, then add either a little tepid water or a little lemon juice if necessary, in order to obtain an ideal consistency: the glaze must be almost solid but you want to be able to spread with a spatula.
Spread the frosting on the cake, leave it for a short while, then enjoy! You can decorate the frosting with walnuts, hazelnuts, almonds, and / or sprinkle with lemon zest.