Preheat your oven to 350°F (180°C). Slice each zucchini in half lengthwise and use a spoon to carefully scoop out the flesh from the center, leaving a sturdy shell with walls about ¼ inch thick. Finely chop the scooped-out zucchini flesh and set aside.
In a saucepan, melt the butter together with 1 tablespoon of the olive oil over medium heat.
Once the butter begins foaming, add the onion and cook gently, stirring occasionally, for 3–5 minutes until it softens and becomes translucent without taking on any color.
Add the chopped zucchini flesh, tomatoes, and basil to the pan. Season with salt and pepper, then cook for 5 minutes, stirring frequently, until the mixture softens and the flavors meld together into a rich filling.
Brush the inside of each hollowed-out zucchini shell with the remaining olive oil. Arrange the shells in a lightly oiled shallow ovenproof dish and place in the oven for 5–10 minutes to partially cook and firm up the shells.
Remove the shells from the oven and spoon half of the tomato mixture evenly into each one. Scatter the chopped capers over the filling, then add a thin layer of cheese. Top with the remaining tomato mixture and finish with a generous layer of the remaining cheese. Return the dish to the oven and bake for 10–15 minutes until the cheese topping is golden, bubbling, and irresistibly melted.