Prep your pan and oven: Heat the oven to 350°F (175°C).
Line a 9x5-inch (23x13 cm) loaf pan with parchment, leaving overhang for easy lifting. Lightly grease the sides.
Mix dry ingredients: In a bowl, whisk flour, baking powder, and salt. Set aside.
Rub zest into sugar: In a large bowl, add sugar and lemon zest.
Use your fingers to rub them together until the sugar is fragrant and slightly damp. This releases more lemon oil for bigger flavor.
Cream butter and sugar: Add softened butter to the lemon sugar. Beat with a hand mixer on medium-high for 3–4 minutes until pale and fluffy.
Add eggs: Beat in eggs one at a time, scraping the bowl.
Mix in vanilla if using. The batter may look slightly curdled—don’t worry.
Combine wet and dry: Add half the flour mixture, then the milk, then the remaining flour. Beat on low just until combined.
Do not overmix.
Bake: Transfer to the prepared pan and smooth the top. Bake for 45–55 minutes, or until a skewer comes out clean and the top is golden. If it browns too quickly, tent with foil for the last 10 minutes.
Make the drizzle: While the cake bakes, stir together lemon juice and sugar until the sugar mostly dissolves.
It should be pourable and slightly gritty.
Pierce and soak: When the cake is done, let it cool in the pan for 10 minutes. Prick the top all over with a skewer or toothpick. Slowly spoon the lemon drizzle over the warm cake so it soaks in.
Cool and set: Let the cake cool completely in the pan, then lift it out.
If using the optional glaze, whisk it smooth and drizzle over the cooled cake for a pretty, tangy finish.