Preheat your oven to 180°C (350°F). Grease your cake pan and line it with parchment paper to prevent sticking.
In a large mixing bowl, whisk together the flour, baking powder, and a pinch of salt to combine evenly.
In another bowl, mix the yogurt, sugar, eggs, and oil until the mixture is smooth, shiny, and slightly frothy—about 1-2 minutes of whisking.
Add the lemon zest and vanilla extract to the wet mixture, stirring gently to incorporate the bright citrus aroma and warmth into the batter.
Gradually fold the dry ingredients into the wet mixture using a spatula, turning gently until just combined. Be careful not to overmix to keep the cake tender.
Pour the batter into the prepared pan and smooth the top with a spatula. Lightly tap the pan on the counter to settle the batter and release air bubbles.
Bake in the preheated oven for 30-35 minutes until the top is golden and cracked slightly. Check doneness by inserting a toothpick into the center; it should come out clean.
Remove the cake from the oven and let it cool in the pan for about 10 minutes before transferring to a wire rack to cool completely. This prevents sogginess and helps set the crumb.
Once cooled, slice the cake with a serrated knife. Serve plain or dusted with powdered sugar, and enjoy its tender, moist crumb with a hint of tang.