Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until al dente, 8 to 10 minutes. Reserve 1 cup of the pasta water and drain well.
In a large bowl, whisk together the olive oil, chile paste, anchovy juice and anchovy fillet.
Add the pasta, top with the grated cheese and toss well, adding enough reserved pasta water to create a sauce. Add the arugula, mint and walnuts, and toss well.
Colatura di alici di Cetara is an Italian anchovy sauce that can be found in specialty shops.