Preheat oven to 350 degrees. Liberally grease a 9"x9" baking pan.
Combine almond butter, honey, and brown sugar in a large bowl.
Grate zucchini on a box grater or in a food processor. Then chop the strands finely, into tiny pieces. Pile the pieces into a thick layer of paper towels (or a clean kitchen towel) and wring to get some of the liquid out. You don't want it dry as sawdust, but if you skip this step your cake will turn out too moist and watery.
Add zucchini to bowl, along with the remaining ingredients. Stir until combined.
Pour into the prepared baking pan. Bake for 40-45 minutes, or until a toothpick comes out clean.