Cook the spaghetti according to the package directions. Drain the pasta and return it to the pot.
Meanwhile, toss the radicchio with the olives, vinaigrette, and ¼ teaspoon each salt and pepper.
Add the cream to the pot with the drained pasta and bring to a simmer.
Add the Pecorino, ½ teaspoon salt, and cracked black pepper and cook, tossing, until thickened and creamy, about 2 minutes.
Top the pasta with additional Pecorino and cracked black pepper, if desired, and serve with the radicchio salad.