Preheat your oven to 360°F and line your cookie sheets with parchment paper. While the oven heats, prepare your zucchini by shredding it and squeezing it thoroughly in a clean kitchen towel or cheesecloth to remove excess moisture—this is crucial because wet zucchini will make your cookies soggy rather than tender. Measure out all your dry and wet ingredients so everything is ready when you need it.
In a large bowl, whisk together the oats, oat flour, ground flax, finely chopped walnuts, cinnamon, ground ginger, baking powder, and salt. Make sure the spices and leavening agents are evenly distributed throughout the dry mixture so every cookie has consistent flavor and rise. I like to sift the cinnamon and ginger together first to break up any clumps before adding them to the bowl—it ensures you won't get pockets of too-strong spice in some cookies.
In a separate bowl, whisk together the room-temperature eggs, honey, oil, applesauce, vanilla, and lemon zest until well combined—the room temperature eggs will mix more smoothly with the other wet ingredients. Pour the wet mixture into your bowl of dry ingredients along with the prepared zucchini, and stir until just combined into a thick, uniform dough. Don't overmix; you want the dough to just come together. I find that the dough is easier to work with if I let it rest for 2-3 minutes after mixing so the oats can absorb some moisture.
Using a 2-tablespoon cookie scoop or measuring spoon, portion the dough onto your prepared cookie sheets, spacing them about 2 inches apart. Gently flatten each portion with the palm of your hand or the bottom of a measuring cup into roughly half-inch thick rounds. The flattening helps the cookies bake more evenly and develop a pleasant texture that's tender inside with slightly crisp edges.
Place the cookies in your preheated 360°F oven and bake for 12-14 minutes, until the edges turn golden brown and the tops are set. The exact time depends on your oven, so start checking around the 12-minute mark. The cookies will continue to firm up slightly as they cool, so don't overbake them or they'll become too dry.
Remove the cookies from the oven and let them rest on the baking sheets for 5 minutes—this allows them to set slightly so they won't fall apart when you move them. After 5 minutes, transfer them to a wire cooling rack to cool completely. Once cool, store them in an airtight container where they'll keep for several days, making them perfect for grab-and-go breakfasts.