Preheat the oven to 170°C and prepare a 16 cm (6-inch) round cake pan with parchment paper.
Whisk 3 eggs, 80g sugar, and 1 tsp vanilla until combined, then warm over a saucepan with 1-2 inches of water until it reaches 40°C.
Melt 25g butter and 25g milk with lemon zest, then whisk the egg mixture on high speed for 6 minutes until it reaches the ribbon stage.
Sift in 90g cake flour in batches, folding gently, then add 7g poppy seeds and mix.
Fold in the butter-milk mixture and pour the lemon cake batter into the pan. Tap to remove air pockets and bake for 35-40 minutes.
Let the cake cool in the pan for a few minutes, then remove and cool completely on a wire rack.