Prep the 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 butter the sides.
Rub zest into sugar. In a large bowl, combine the sugar and lemon zest. Use your fingers to rub them together until the sugar is fragrant and slightly damp. This releases the oils and boosts lemon flavor.
Cream the butter and lemon sugar. Add the softened butter to the bowl.Beat with a hand mixer or whisk until light and fluffy, 2–3 minutes. Scrape the bowl.
Add eggs and vanilla. Beat in the eggs one at a time until smooth. Mix in the vanilla, if using.The batter may look slightly curdled—don’t worry.
Combine dry ingredients. In a separate bowl, whisk the flour, baking powder, and salt.
Alternate dry and wet. Add half the dry mix to the batter and mix gently. Stir in the milk or buttermilk. Add the remaining dry mix and fold just until no streaks remain. Do not overmix.
Bake. Scrape the batter into the pan and smooth the top.Bake 45–55 minutes, until a skewer inserted in the center comes out with just a few moist crumbs. If the top browns too fast, tent loosely with foil in the last 10 minutes.
Make the drizzle. While the cake bakes, stir the lemon juice and sugar in a small bowl until the sugar mostly dissolves.
Soak while warm. Let the loaf cool in the pan for 10 minutes. Poke holes all over with a skewer or toothpick.Slowly spoon the lemon drizzle over the warm cake, letting it sink in. Use every drop.
Cool and glaze (optional). Lift the cake out and cool completely on a rack. For a glossy top, whisk powdered sugar with lemon juice to a pourable glaze and drizzle over the cooled loaf.Let it set for 15 minutes before slicing.