Preheat the oven to 350 degrees. In a large bowl, beat the butter and sugars together until light in color and very fluffy, about 3 to 5 minutes.
Add the vanilla and eggs and beat for another minute.
Add the grated zucchini and mix until incorporated.
Sprinkle the flour, cinnamon, baking powder, baking soda, and salt over the wet ingredients. Mix everything together on low speed until well combined. Add the rolled oats and mix to combine.
Scoop dough into balls using a 1-ounce cookie scoop and place on a baking mat or parchment-lined baking sheet.
Bake for 12 to 16 minutes until the center is set and the edges are golden. Let the cookies rest on the cookie sheet for 5 minutes before transferring them to a wire rack. Store covered.
Notes
I like to use old fashioned rolled oats in these cookies but you could also use quick cooking oats (also called 1-minute oats).
If you use white all-purpose flour instead of whole wheat flour, you will need to add about ⅓ cup more to the recipe.
Store baked cookies in an airtight container with a piece of waxed or parchment paper between each layer (or the cookies will stick together).