Use a vegetable peeler to peel long ribbons of zucchini.
Heat a skillet over medium-high heat and heat butter and olive oil. Add the zucchini ribbons and toss around the pan for 1 - 2 minutes. Sprinkle with salt and pepper. Add the tomatoes and parmesan cheese. Toss to heat everything up.
Serve within a few minutes, before the zucchini gets too soft.