Preheat your oven to 375°F (190°C) and prepare a cookie sheet by greasing it or lining it with parchment paper.

In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until evenly combined.

Cream the softened unsalted butter and granulated sugar together on medium speed for about 2-3 minutes until light and fluffy.

Add in the egg and freshly grated lemon zest and continue mixing for an additional 2-3 minutes.

Gradually mix the flour mixture into the wet ingredients until just combined, being careful not to overmix.

Gently fold in the grated zucchini with a spatula until evenly distributed.

Drop rounded tablespoonfuls of dough onto the prepared cookie sheet, spacing them about two inches apart.

Bake for 10-12 minutes until lightly browned around the edges and soft in the center.

Allow cookies to cool on the baking sheet for about 5 minutes before transferring to a wire rack.

Prepare the glaze by mixing powdered sugar and lemon juice until smooth, then drizzle over each cookie once cooled.