Preheat the oven to 350°F and line a baking dish with parchment paper.
Shred the zucchini and carrots, then gently press out extra liquid with a clean towel.
In a large bowl, whisk together eggs, honey, melted coconut oil, and vanilla.
Stir in shredded zucchini and carrots.
Add oats, flour, baking powder, cinnamon, and salt. Mix until well combined.
Pour the batter into the prepared baking dish and spread evenly.
Bake for 25–30 minutes until the top is set and lightly golden.
Cool completely before slicing into bars.