Preheat the oven to 350 degrees F and line two baking sheets with parchment paper.

Grate the zucchini on the large holes of a box grater. Wrap the shreds in a clean kitchen towel and squeeze out as much moisture as you can over the sink. Measure out 1 cup of the pressed zucchini and set it aside.

Lightly crush the dried lavender between your fingers before measuring. You want it broken up enough to release the aromatic oils without turning it into powder. In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and crushed lavender.

In a large bowl, beat the softened butter and granulated sugar together on medium speed for about 2 minutes until pale and fluffy. Add the egg, vanilla, and milk, and beat for another 30 seconds until smooth.

Add the flour mixture to the butter mixture and stir until just combined. Fold in the squeezed zucchini and stir gently until the shreds are evenly mixed through the dough. The dough will be soft.

Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them 2 inches apart. Lightly flatten each with your palm or the back of a spoon. They will not spread very much on their own.

Bake for 10 to 11 minutes until the edges are just barely set and the tops look dry but not golden. Pull them from the oven right at this point. Over-baking will make them dry and the lavender flavor less pleasant.

Immediately after pulling the pans from the oven, drizzle a small amount of honey over each cookie using a spoon. The warmth of the cookie helps the honey soak in slightly. Let them sit on the pan for 5 minutes, then transfer to a wire rack to finish cooling.