Preheat your oven to 350°F (175°C). Grease a cake pan.
In a mixing bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and poppy seeds.
In another bowl, combine the eggs, Greek yogurt, oil, lemon zest, lemon juice, and vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until just combined.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 35 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.