Using a food processor, finely chop the cheese; transfer to a bowl. Add the walnuts to the processor; finely chop. Add to the cheese.
Bring a pot of salted water to a boil. Fill a bowl with ice water. Boil the broccolini for 3 minutes. Drain; add to the ice water. Drain and finely chop.
Transfer the broccolini to a large bowl. Toss with the radicchio, arugula, currants, cheese and walnuts. Drizzle with the vinegar and EVOO; toss and season with sea salt and pepper.