Start by finely shredding the zucchini and squeezing it dry with a clean kitchen towel—this removes excess moisture that would make your muffins soggy. While you're doing this, make sure your eggs are at room temperature as they'll blend more smoothly into the batter. In a large bowl, mash the very ripe bananas until mostly smooth with a few small lumps remaining for texture. Stir in the room-temperature eggs, applesauce, and vanilla extract until well combined, then fold in the prepared zucchini. This wet mixture is now ready to combine with your dry ingredients.
In a separate bowl, whisk together the flour, sugar (or monk fruit sweetener), cinnamon, nutmeg, baking powder, baking soda, and salt. Whisking rather than just stirring helps distribute the leavening agents evenly throughout the flour, which ensures your muffins rise consistently. I like to sift my flour first if I have time—it prevents dense pockets in the finished muffins, though whisking works well too.
Pour the dry ingredient mixture from Step 2 into the wet banana-zucchini mixture from Step 1. Fold everything together gently using a spatula or wooden spoon, stirring just until the dry ingredients are moistened—the batter should look slightly lumpy. Overmixing develops gluten and creates tough, dense muffins, so stop as soon as you don't see streaks of dry flour. If using walnuts, fold them in now for an even distribution.
Preheat your oven to 350°F. Lightly grease a standard 12-cup muffin pan with cooking spray or oil. Divide the batter evenly among the cups, filling each about two-thirds full—this gives the muffins room to rise without overflowing. Bake for 22-26 minutes until a toothpick inserted into the center comes out clean or with just a few moist crumbs. I find that my oven typically needs the full 26 minutes, so start checking at the 22-minute mark rather than assuming the lower time will work.
Allow the muffins to cool in the pan for 5-10 minutes—this helps them firm up so they won't fall apart when you remove them. Run a small knife or offset spatula around the edges of each muffin to loosen them, then gently turn them out onto a wire rack to cool completely. Store in an airtight container at room temperature for up to 3 days, or freeze for longer storage.