Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving an overhang on two sides for easy removal. Lightly coat with nonstick baking spray.
Shred the zucchini using the large holes of a box grater. Sprinkle the shredded zucchini with salt and let it sit for 10 minutes. Place the zucchini in a clean kitchen towel or colander and squeeze out as much excess moisture as possible. Set aside.
In a large bowl, whisk together the old-fashioned oats, oat flour, all-purpose flour, baking powder, kosher salt, cinnamon, and ground flaxseed.
In a separate medium bowl, whisk together the brown sugar, egg, whole milk, melted butter, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the shredded zucchini and 1¾ cups of the chopped chocolate, being careful not to overmix.
Spread the batter evenly into the prepared baking pan. Sprinkle the remaining ¼ cup chopped chocolate over the top.
Bake for 30–38 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out with a few moist crumbs but no wet batter.
Allow the bars to cool in the pan for 20–30 minutes before lifting them out using the parchment paper. Slice into 16 bars and enjoy.