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Preheat your oven to 180°C (350°F). Grease a cake pan or line it with parchment paper.
In a large bowl, beat the eggs and sugar together until the mixture becomes light and fluffy.
Add the vanilla extract, vegetable oil, and yogurt. Mix well until combined.
In a separate bowl, sift together the flour, baking powder, and salt.
Gradually fold the dry ingredients into the wet mixture until just combined, avoiding overmixing.
Pour the batter into the prepared cake pan and smooth the surface.
Bake for about 25–30 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool before slicing.
Serving and storage tips:
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