Bring a large pot of salted water to a boil. in a large skillet, heat 1/4 cup EVOO over medium heat. Add the garlic and cook until sizzling and golden around the edges, about 2 minutes. Add the crushed red pepper; toast for 1 minute. Add the tomatoes, celery and 1/2 tsp. salt. Fill the tomato can with 1 cup pasta water and swish to collect any remaining tomato juices; add to the skillet. Bring the sauce to a boil. Stir in the olives, lower the heat and simmer until thickened, about 10 minutes. Add the capers and parsley and simmer for a few minutes.
When the sauce is about halfway done, add the pasta to the boiling water. Cook until al dente; drain and add the pasta to the sauce, tossing to coat. Continue cooking and tossing the pasta in the sauce until well coated. Drizzle with the remaining 2 tbsp. EVOO; toss again. Remove from the heat, then toss with the cheese.