Wash the zucchini, cut off the ends and dice.
Briefly fry the garlic in olive oil, in a large pan. Add the zucchini, season with salt, stir and sauté over low heat with a lid on until the zucchini are soft, stirring occasionally.
Boil the spaghetti in a large pot of salted water until al dente.
Add 1-2 tbsp of the water in which the pasta was cooked to the zucchini. Add the sweet cream and then the grated cheese. Stir until the cheese melts and season with salt and pepper to taste.
Add the drained spaghetti to the zucchini and toss until the sauce covers the pasta. Sprinkle with olive oil to your liking prior to serving.