Preheat the oven to 350°F. Line two baking sheets with parchment paper.
In a large mixing bowl, combine the grated zucchini, granulated sugar, brown sugar, vegetable oil, eggs, and vanilla extract. Mix until well blended.
In another bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. If using, fold in the chopped nuts and chocolate chips.
Drop tablespoon-sized scoops of dough onto the prepared baking sheets, spacing them about 2 inches apart. Bake for 12-15 minutes, or until the edges are lightly golden. Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to wire racks to cool completely.
While the cookies are cooling, prepare the filling. In a medium bowl, beat the softened butter until creamy. Gradually add the powdered sugar, vanilla extract, and milk, mixing until smooth and fluffy.
Once the cookies are completely cool, spread a generous amount of filling on the flat side of one cookie and top with another cookie to create a sandwich. Repeat with the remaining cookies.
Notes
These cookies can be stored in an airtight container at room temperature for up to 3 days.
For a healthier version, substitute half of the all-purpose flour with whole wheat flour.
Add a pinch of sea salt to the filling for a sweet and salty flavor contrast.