Prep the pan and oven. Heat the oven to 180°C/160°C fan (350°F).
Line a 9x13-inch (23x33 cm) traybake tin with baking paper, leaving an overhang for easy lifting.
Cream butter and sugar. In a large bowl, beat the softened butter and sugar with an electric mixer for 2–3 minutes until pale and fluffy. This step helps create a light crumb.
Add eggs and flavorings. Beat in the eggs one at a time, mixing well after each. Stir in vanilla, lemon zest, and lemon juice.
The mixture may look slightly curdled—this is normal and will smooth out once dry ingredients are added.
Combine dry ingredients. In a separate bowl, whisk together flour, baking powder, and salt.
Alternate dry ingredients and milk. Add half the dry ingredients to the butter mixture, then half the milk. Repeat with the remaining dry ingredients and milk. Mix on low just until combined. Do not overmix.
Fill the tin. Scrape the batter into the lined tin and spread it evenly to the edges.
Tap the tin lightly on the counter to release air bubbles.
Bake. Bake for 22–28 minutes, or until the top is lightly golden and a skewer inserted in the center comes out clean. The edges should spring back when touched.
Make the glaze. While the cake bakes, whisk the icing sugar with 3 tbsp lemon juice. Add more juice a little at a time until it’s thick but pourable—like heavy cream.
Glaze while warm. Let the cake cool in the pan for 10 minutes.
Poke small holes across the surface with a skewer, then pour over the glaze and spread to the corners. It will seep in and set with a slight sheen.
Cool and slice. Allow to cool completely in the tin before lifting out and cutting into squares. Decorate with extra zest or thin lemon slices if you like.