Preheat oven to 350 degrees F. Lightly grease a 9x5-inch loaf pan.
Whisk flour, baking soda, cinnamon, ginger, and nutmeg together in a bowl until well combined.
Stir sourdough discard in a second bowl. Let sit until bubbles start to form, about 5 minutes.
Meanwhile, place grated zucchini in a third bowl. Sprinkle with salt and toss to combine. Let sit for 5 minutes.
Gently squeeze small handfuls of zucchini over the sink to drain any liquid. Transfer zucchini to a large mixing bowl and add mashed banana, brown sugar, and oil. Whisk until zucchini is evenly distributed and no lumps of brown sugar remain. Stir in sourdough discard until evenly distributed. Add flour mixture gradually, stirring until just incorporated. Pour into the prepared loaf pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 55 to 60 minutes. Remove from the oven and let cool in the pan for 5 minutes. Transfer loaf to a wire rack and cool completely before slicing, about 30 minutes.