For the Pistachio Pesto: Combine the parsley, pistachios, thyme, and garlic cloves in the bowl of a food processor; blend until finely chopped. With the machine running, gradually add the olive oil, processing until well blended. Season the pesto with salt and pepper, to taste.
For the Fennel Slaw: Place the fennel in a large serving bowl. Add the pesto and toss to coat well. Tear the prosciutto into 1-inch pieces and add to the bowl. Gently toss to combine. Serve.