Preheat the oven to 340F (170C). Grease and line the bottom of an 8-inch (20 cm) pan with parchment paper.
Separate whites from yolks.
In a medium bowl mix yolks with 1/3 cup (70g) sugar, lemon zest and vanilla extract, until creamy and pale yellow colored. Add baking powder and mix to combine. Gradually mix in oil and then add water.
Incorporate flour and poppy seeds.
In a large bowl mix egg whites with salt until foamy. Gradually add the remaining 1/3 cup (70g) sugar. Continue mixing until stiff peaks form.
Gently fold a spoon of whipped whites into the yolk mixture and then gently fold the yolk mixture into the whipped whites.
Pour the batter into the prepared pan.
Bake for 35-40 minutes, until a toothpick inserted into the center comes out clean.
Let it cool for about 10-15 minutes. Remove from the pan, invert and cool completely on a rack.