Heat oven to 350 degrees and line a large cookie sheet with parchment (or grease a pan).
Chop the shredded zucchini even smaller (optional) and transfer to a tea towel to soak extra moisture while proceeding with the recipe (do not wring or press, just let it release moisture).
Melt butter and chocolate chips in microwave 30 to 45 seconds, stirring until all the chips are melted (or use a saucepan over low heat just until melted, whisking to smooth).
Stir in brown sugar, white sugar, and cocoa powder until combined.
Add yogurt or sour cream and vanilla, stirring well.
Mix in flour, soda, and salt until no streaks remain - the dough will be thick.
Then add the shredded zucchini, stirring until it's all incorporated.
Using a tablespoon sized cookie scoop, drop the dough onto the prepared cookie sheet. Add a few chocolate chips to the top of each cookie, pressing lightly as you do.
Bake for 8 minutes only. Let cool on cookie sheet for about 5 minutes before removing to a cooling rack to cool completely.
Store in an airtight container or freeze for longer storage.*
Notes
*If layering cookies for storage, add a piece of parchment or waxed paper between the layers - the moistness of the cookies will cause them to stick together.