Preheat the oven to 350°F.
Spray an 8x8-inch baking pan with nonstick cooking spray, then line with parchment paper, leaving a little excess hanging over the edges on all four sides. Set aside.
Combine the granulated sugar and lemon zest in a large bowl. Use your fingers to massage the lemon zest into the sugar until the zest starts to melt into the sugar and the mixture is very fragrant, about 1 minute.
To the sugar-lemon zest mixture, add the yogurt, eggs, oil, and 3 tablespoons of lemon juice (save the remaining juice for the glaze, if you’re making it). Whisk until smooth.
Add the flour, baking powder, salt, and baking soda. Switch to a rubber spatula and fold the dry ingredients into the wet until no streaks of flour remain.
Scape the batter into the prepared pan and smooth the top into an even layer.
Bake until the cake is domed in the center and a cake tester inserted in the center comes out clean, 35 to 45 minutes.
Let the cake cool in the pan on a wire rack for 30 minutes.
While the cake cools, make the glaze, if desired. Clean and dry the bowl used to make the cake. Add the sifted powdered sugar to the bowl, then add 1 ½ tablespoons of the reserved lemon juice. Whisk until smooth.
When the cake is fully cool, set it on top of a serving platter and add the glaze on top, if using. Use an offset spatula or spoon to encourage the glaze towards the edges, then let it drip down the sides naturally. Cut into pieces and serve.
