Heat olive oil in a skillet over medium heat; cook and stir mushrooms in the hot oil until slightly softened, 5 to 10 minutes. Add marinara sauce, tomato, olives, green bell pepper, red bell pepper, artichoke heart, garlic, basil, salt, and pepper to mushrooms; bring to a boil. Simmer until tomato sauce is heated through, 5 to 10 minutes.
Bring a large pot of lightly salted water to a boil. Cook cavatappi in the boiling water, stirring occasionally until cooked through but firm to the bite, 8 minutes. Drain and transfer to a serving bowl.
Sprinkle mozzarella cheese over cavatappi. Pour tomato sauce over mozzarella layer; sprinkle with Parmesan cheese.