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Preheat your oven to 180°C (350°F). Grease and lightly flour a 9-inch round cake pan or line it with parchment paper.
In a large bowl, whisk together the eggs and sugar until the mixture becomes pale and slightly frothy. Add the yogurt, vegetable oil, and vanilla extract (plus lemon zest if using). Mix until well combined.
Sift the flour, baking powder, and salt together. Gradually add the dry ingredients to the wet mixture. Stir gently with a spatula or wooden spoon until just incorporated. Avoid overmixing to ensure the cake remains light and tender.
Pour the batter into the prepared pan. Tap the pan gently on the counter to remove any air bubbles. Bake in the preheated oven for 30–35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes. Then transfer it to a wire rack to cool completely before slicing.