Using a vegetable peeler, peel the zucchini into long ribbons.
Set a nonstick skillet over medium-high heat and heat the butter and olive oil. Add the zucchini and toss around in the skillet for 1 to 2 minutes. Sprinkle in some salt and pepper. Add the Parmesan, tomatoes and garlic and toss to heat through. Sprinkle over the basil and serve within a few minutes, before the zucchini gets too soft!