Preheat your oven to 180°C (350°F). Grease a 23cm round cake pan and line the bottom with parchment paper.
In a large mixing bowl, whisk together the homemade strained yogurt, sugar, and eggs until the mixture is smooth, slightly frothy, and fragrant, about 2 minutes.
Add the vegetable oil to the wet mixture and whisk until fully incorporated, creating a glossy batter.
Sift together the all-purpose flour and baking powder into the bowl, then gently fold the dry ingredients into the wet mixture using a spatula, just until no streaks remain. Be careful not to overmix to keep the batter airy.
If using, fold in the lemon zest for a fresh, citrusy aroma that complements the tang of the yogurt.
Pour the batter into your prepared cake pan, smoothing the top with a spatula to ensure even baking. Gently tap the pan on the counter to release any air bubbles.
Bake in the middle of the oven for 30–35 minutes, until the top is golden and a toothpick inserted into the center comes out with moist crumbs, not wet batter.
Remove the cake from the oven and let it cool in the pan for about 10 minutes. Then, transfer it to a wire rack to cool completely, allowing the crumb to set and develop moisture.
Once cooled, dust the top with powdered sugar or serve with fresh berries. Slice with a serrated knife for clean cuts and enjoy the tender, tangy crumb with a hint of citrus aroma.