How to Make It
Preheat the oven to 350°. Spray a 9-inch square metal baking pan with nonstick cooking spray and line the pan with parchment paper. In a medium bowl, whisk the flour with the baking powder and salt. In a small bowl, combine the superfine sugar with the lemon zest; rub the zest into the sugar until the sugar is slightly damp and aromatic.
In a stand mixer fitted with the paddle, beat the butter at medium speed until smooth, about 2 minutes. Add the lemon sugar and beat until light and fluffy, 3 minutes more. Add the eggs one at time, beating well after each addition. At low speed, beat in the dry ingredients just until incorporated.
Scrape the batter into the prepared pan and smooth the surface. Bake for 30 to 35 minutes, until the cake is golden and a toothpick inserted in the center comes out clean. Transfer the cake to a rack.
Whisk the granulated sugar with the lemon juice until the sugar has dissolved. Using a fork, poke 1-inch-deep holes all over the warm cake. Pour half of the lemon syrup over the cake and let it soak in for about 3 minutes, then pour the remaining syrup over the cake. Let cool for 30 minutes.
Run a thin knife around the edge of the cake and invert it onto a work surface. Discard the parchment. Turn the cake right side up on the rack and let cool completely.
In a microwave-safe bowl, combine the lemon juice with the granulated sugar and microwave at high power for 30 seconds, until the sugar is mostly dissolved and the syrup is steaming. Scrape the syrup into a medium bowl. Add the confectioners’ sugar and butter and whisk until smooth. Pour the glaze over the cooled cake and let stand until the glaze is set, about 15 minutes.