Preheat your oven to 350°F (175°C). Grease and flour a cake pan.
In a mixing bowl, whisk together the Greek yogurt, sugar, and eggs until smooth.
Add the vegetable oil, vanilla extract, and lemon zest. Mix well.
In another bowl, combine the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the poppy seeds.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.