Start the broiler in your oven and line a rimmed baking sheet with foil.Slice the mini zucchini in half or larger zucchini into sticks.Over high heat, add the butter and oil to a heavy bottom pan. When the fat is hot, add in the zucchini cut side down. Allow to brown for 2-3 minutes. Add in the red onion, reduce the heat to medium and cover. Continue to cook for 5-7 minutes.When the zucchini are tender, remove from the pan with tongs and add to the baking sheet with the cut side up. Keep them close together. Spread the cooked onions on top, spray with some balsamic vinegar and sprinkle the grated parmesan liberally over the top.Place the zucchini under the broiler for 2-3 minutes or until the cheese is melted and browned slightly.Remove carefully from the pan and add to a dish. Drizzle reduced balsamic overtop and sprinkle with some of the basil.Enjoy hot or at room temperature. Happy eating!