Rinse the zucchini under cold water. Remove the stem and discard. Cut into ½ inch dices. Set aside.
In a large skillet, over medium heat, sauté the onion in half of the butter and the olive oil until translucent. Add the zucchini and cook together until lightly golden. Add the rice and stir together until opaque and lightly toasted. Add the wine and allow to evaporate. Add a ladle of the warm stock. Continue to cook and stir (preferably with a fork) until the liquid is almost fully absorbed. As the liquid absorbs, add more stock, a ladle at a time, waiting until almost completely absorbed before adding more. Cook until rice is al dente, about 10-15 minutes, and creamy.
Mix in the cheese. Remove the skillet from the heat. Serve immediately with some fresh black pepper.