Mash 2 medium bananas in a large bowl with a fork or potato masher until smooth with just a few small lumps (3/4 cup mashed). Reserve 2 tablespoons shredded zucchini and add the remaining zucchini, melted butter, 1 large egg, 1/2 cup packed light brown sugar, 1/2 cup granulated sugar, and 2 teaspoons vanilla extract. Whisk to combine.