Before you start baking, grease and flour a sheet pan. Pre-heat oven to 340 °F (170 °C).
In a large mixing bowl, crack an egg, add vegetable oil and granulated sugar. Mix with a hand-held kitchen mixer for 3 minutes.
In a separate bowl, whisk flour, poppy seeds, and baking powder. Add them to the beaten egg. Add milk and mix everything using a mixer on low speed until a semi-liquid batter is created.
Pour and spread the batter evenly into the prepared pan.
Bake for 30 minutes. To test for doneness, insert a toothpick into the cake center. The tooth stick needs to come out clean, or with a few crumbs stuck to the tooth stick, then the cake is finished.
Set the baked cake aside. Meantime, make a smooth lemon icing. To achieve this, mix sifted icing sugar with freshly pressed lemon juice. Drizzle the lemon icing over warm cake and spread it using a tablespoon.
Allow the cake to cool completely in the pan. Slice and serve as a dessert or a coffee cake.