Preheat oven to 325 degrees F. Grease a 9x5;-inch loaf pan and line it with parchment, so that excess parchment hangs over each side.
Place the zucchini in a clean dish towel, gather together and twist and squeeze to drain out as much liquid as possible.
In a medium bowl, whisk together the brown sugar, oil, eggs and vanilla extract. Fold in the drained zucchini.
In a large bowl, whisk the all-purpose flour, whole wheat flour, cinnamon, salt, baking powder, baking soda and nutmeg. Add the zucchini mixture and fold together until just a few streaks of flour remain. Add the walnuts and cranberries to the batter and gently fold to combine.
Pour the batter into the prepared pan and sprinkle the granulated sugar evenly over the top.
Bake until a toothpick inserted in the center comes out with a few moist crumbs attached, 65 to 75 minutes. Allow the bread to cool in the pan on a wire rack for 30 minutes. Remove the bread from the pan and allow to cool completely on a wire rack before serving. Leftover bread should be wrapped tightly in plastic wrap and stored at room temperature for up to 4 days.