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Preheat the oven to 350° F, line the bottom of a round 25-cm (10-inch) cake pan with parchment paper and grease the sides.
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In a large mixing-bowl, gently combine the yogurt, eggs, sugar, vanilla, oil.
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In another bowl, sift together the flour, baking powder, baking soda, lemon zest, and poppy seed.
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Add the flour mixture into the yogurt mixture, and blend together -- don't overwork the dough.
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Pour the batter into the prepared cake pan, and bake for 30 to 35 minutes, until the top is golden brown and a cake tester comes out clean.
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Let stand for ten minutes, and transfer onto a rack to cool.