Heat olive oil in a large saucepan over medium heat. Add onion, garlic, and chile pepper; cook until onion has softened and turned translucent, about 5 minutes. Increase heat to medium-high; stir in cherry tomatoes. Cook until tomatoes start to break down and begin to make a sauce, about 5 minutes. Stir in crushed tomatoes; bring to a simmer, then reduce heat to medium-low and cook for 10 minutes.
Meanwhile, bring a large pot of lightly salted water to a boil over high heat. Cook gnocchi in the boiling water until they float to the top, 2 to 3 minutes. Gently transfer gnocchi to a serving dish using a strainer or slotted spoon.
Stir basil and olives into simmering sauce; cook 1 minute. Pour sauce over gnocchi. Sprinkle servings with Parmesan cheese.
