Preheat oven to 350F. Line a large baking sheet with parchment paper. Shred zucchini on the fine side of a box grater, then wrap in a clean kitchen towel and squeeze firmly to remove excess moisture. You want about 1 cup firmly packed, fairly dry zucchini.

In a large bowl, whisk together melted butter, maple syrup, egg, and vanilla until smooth. Stir in the squeezed-dry zucchini until evenly distributed.

Add oats, whole wheat flour, baking powder, cinnamon, nutmeg, and salt to the bowl. Stir with a wooden spoon until no dry spots remain and a thick, sticky dough forms. Let rest 5 minutes so the oats absorb some moisture.

Scoop generous 3-tablespoon mounds of dough onto the prepared baking sheet, spacing 2 inches apart. Gently flatten each mound into a 2.5-inch round about 0.5-inch thick - they won't spread much.

Bake until the edges are set and lightly golden and the centers look dry with small cracks, 12 to 14 minutes. The cookies will still feel soft - that's correct. Cool on the pan 10 minutes, then transfer to a wire rack to cool completely.