Heat your oven to 350 degrees F. Line two baking sheets with parchment paper and set them aside.

Grate the zucchini on the large holes of a box grater. Scoop it into a clean kitchen towel or a few layers of cheesecloth, wrap it up, and squeeze firmly over the sink until very little liquid comes out. You want the zucchini as dry as possible so the cookies hold their shape. Measure 1 cup of the squeezed zucchini and set aside.

In a large bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon until combined. Push the dry ingredients to the sides to make a well in the center.

Add the softened butter and brown sugar to the well. Use a sturdy spoon or your hands to beat them together until the mixture looks creamy and slightly fluffy, about 2 minutes of vigorous stirring. Add the egg and vanilla and stir until everything is smooth.

Fold the dry ingredients into the wet ingredients until just combined, then fold in the squeezed zucchini, dried cherries, and pistachios. The dough will be soft and a little sticky. Do not overmix once the flour goes in.

Scoop the dough by rounded 2-tablespoon portions onto the prepared baking sheets, spacing them about 2 inches apart. These cookies spread a little but not dramatically.

Bake one sheet at a time on the center rack for 11 to 13 minutes, until the edges are set and lightly golden and the centers look just barely done. They will firm up as they cool. Do not wait for them to look fully dry on top or they will overbake.

Let the cookies rest on the baking sheet for 5 minutes before moving them to a wire rack to cool completely. The texture settles nicely as they cool and the tops will look slightly crinkled.