Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
Shred zucchini using a box grater and pat lightly with paper towels.
In a bowl, whisk flour, oats, cinnamon, baking soda, and salt.
In a large bowl, beat butter and brown sugar until light and fluffy.
Add egg and vanilla extract and mix until smooth.
Gradually add dry ingredients to wet ingredients and stir until combined.
Fold in shredded zucchini and any optional add-ins.
Drop spoonfuls of dough onto prepared baking sheets.
Bake 10–12 minutes until edges are lightly golden and centers remain soft.
Cool cookies on baking sheet for several minutes before transferring.
If desired, drizzle glaze over cooled cookies before serving.
