Prepare. Preheat the oven to 350°F (180°C). Grease an 8-inch round pan or loaf pan and line the bottom with parchment paper.
Mix the dry ingredients. Whisk the flour, baking powder and salt in a bowl.
Flavor the sugar. In a large bowl, rub the lemon zest into the sugar with your fingers until fragrant.
Mix the wet ingredients. Whisk the eggs into the sugar until smooth, then whisk in the yogurt, oil, lemon juice and vanilla.
Combine. Add the dry ingredients to the wet and stir just until no streaks of flour remain. Don't overmix.
Bake. Pour the batter into the pan and bake 40 to 50 minutes, until golden and a toothpick inserted in the center comes out clean.
Cool. Let the cake rest in the pan for 10 minutes, then turn it out onto a rack to cool completely.
Glaze (optional). Stir the powdered sugar with enough lemon juice to make a thick, pourable glaze. Spoon it over the cooled cake.