Dice the carrot, then thinly slice the leek and the onion, crush the garlic, and dice the zucchini.
Melt the butter in a large saucepan over medium heat. Add the oil, then sauté the onion for 4 to 5 minutes, until it's soft and translucent. Add the leek, carrot, and garlic, and sauté for another 2 to 3 minutes until the leek has softened.
Stir in the rice and cook for 1 minute, then stir in a ladleful of broth and cook slowly until the liquid is absorbed, stirring all the time.
Add the rest of the broth a ladleful at a time -- wait until it is absorbed before adding more. Stir the rice regularly during cooking. After about 18 minutes it will be almost cooked through.
Add the diced zucchini and peas, plus more broth if necessary. Cook for another 4 minutes, or until the vegetables are cooked through. Remove from the heat and stir in the cheese. Season with pepper, then serve.