Preheat the oven to 350ºF. Line a 9×5-inch loaf pan with parchment paper and set aside.
Put the dry ingredients in a bowl and whisk to combine. Add eggs, banana, oil, honey, and vinegar and beat until smooth. Fold in the cranberries.
Transfer the batter to the prepared pan, sprinkle with turbinado sugar and bake on the center rack for 40-45 minutes, until the top has turned golden brown and a cake tester inserted into the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack and cool completely before slicing.