Heat olive oil in a large saucepan over medium heat. Stir in the onion, garlic and chilli and cook until the onion has softened and turned translucent, about 5 minutes. Increase heat to medium-high and stir in the cherry tomatoes. Cook until the tomatoes have lost their form and are beginning to make a sauce, about 5 minutes. Stir in the crushed tomatoes, bring to a simmer, then reduce heat to medium-low and cook for 10 minutes.
While the sauce is simmering, bring a large pot of lightly salted water to a boil over high heat. Add the fresh gnocchi and cook until the gnocchi float to the surface, 2 to 3 minutes. Gently strain out the gnocchi and place into a serving dish.
Stir the basil and olives into the simmering sauce and cook for one minute. Pour the sauce over the drained gnocchi and serve with Parmesan cheese.