Preheat the oven to 350°F (175°C). Grease and line a loaf pan or an 8-inch round cake pan with parchment paper.
In a large bowl, whisk together yogurt, sugar, eggs, oil, and vanilla extract until smooth.
In a separate bowl, combine flour, baking powder, salt, and any zest if using.
Fold the dry ingredients into the wet ingredients gently until just combined. Do not overmix.
Pour the batter into the prepared pan and smooth the top.
Bake for 35–40 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.