Core tomatoes; holding them over a nonreactive mixing bowl, cut into 1-inch chunks, catching any juice in the mixing bowl. Sprinkle with salt.

Put olive oil, olives, garlic, and anchovies in the bowl of a food processor and pulse, scraping down the sides occasionally, until finely chopped. Scrape into the bowl with the tomatoes and combine; cover and set aside to marinate for several hours, stirring occasionally.

Cook the pasta and drain, reserving 1/2 cup cooking water. Immediately add the hot pasta to the marinated tomatoes and toss; the hot pasta will soak up some of the tasty juice. Stir in the baby greens, Italian sausage, roasted tomatoes, and basil; gently fold in the artichoke hearts and drizzle with additional olive oil if desired. Serve hot or cold.