Step 1

Arrange a rack in the middle of the oven and heat the oven to 350ºF. Coat an 8x4- or 9x5-inch loaf pan with cooking spray. Line the bottom and 2 long sides of the pan with a sheet of parchment paper that extends over the sides by a few inches to form a sling.

Step 2

Melt 1 stick unsalted butter in the microwave or stovetop.

Step 3

Finely grate the zest of 2 medium lemons into a medium bowl (about 2 teaspoons); reserve 1 of the zested lemons for the glaze. Add 1/2 cup granulated sugar and rub the zest into the sugar with your fingers until fragrant. Add the butter, 1 cup packed light brown sugar, 2 large eggs, 2 teaspoons vanilla extract, and 3/4 teaspoon kosher salt. Whisk until smooth and lightened in color.

Step 4

Place 2 cups all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, and 1/2 teaspoon ground cinnamon in a large bowl and whisk to combine.

Step 5

Trim and grate 1 pound zucchini on the large holes of a box grater (3 to 4 cups). Place about 1/3 of the zucchini on a clean kitchen towel. Gather up the sides and squeeze over the sink to press out as much moisture from the zucchini as possible. Add to the flour mixture. Repeat with the remaining zucchini in two more batches. Stir the zucchini into the flour with a flexible spatula until combined with no big clumps of zucchini.

Step 6

Add the sugar mixture and fold together with the spatula until just combined with no streaks of dry flour remaining; the batter will be very thick. Transfer to the loaf pan and spread into an even layer.

Step 7

Bake until golden-brown on top and a tester inserted in the center comes out clean, 1 hour and 5 minutes to 1 hour and 20 minutes. Let cool for 15 minutes in the pan. Grasping the excess parchment, lift the cake out of the pan and place on a wire rack. Let cool completely before glazing, about 2 hours.

Step 8

Juice the reserved lemon until you have 1 1/2 tablespoons. Place the lemon juice and 1 cup powdered sugar in a medium bowl and whisk until a thick, smooth glaze forms. Drizzle over the cake and let sit until the glaze sets, about 15 minutes.