Preheat the oven to 350°F (175°C). Grease an 8-inch round cake pan and line the bottom with parchment paper.
Place the sugar in a large mixing bowl. Add the lemon zest and rub it into the sugar using your fingertips until fragrant and lightly yellow. This helps release the natural citrus oils.
Add the flour, baking powder, baking soda, and salt to the lemon sugar. Whisk until evenly combined.
In another bowl, whisk together the sunflower oil, egg, yogurt, milk, lemon juice, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients.
Fold gently with a spatula until no dry flour remains. Avoid overmixing to keep the cake tender.
Spread the batter evenly into the prepared cake pan.
Bake for 25–30 minutes, or until the top is lightly golden and a toothpick inserted into the center comes out clean.
Cool the cake in the pan for 20 minutes before transferring it to a wire rack.
To prepare the glaze, whisk together the powdered sugar, yogurt, and lemon juice until smooth.
Place the cooled cake on a wire rack set over a baking tray or parchment paper.
Pour the glaze over the cake, allowing it to drip naturally over the edges.
Sprinkle additional lemon zest over the glaze while it's still wet.
Allow the glaze to set before slicing and serving your Lemon Yogurt Cake.