In a food processor, pulse all pesto ingredients until smooth. Set aside.
Cook the pasta al dente. In the last minute of cooking, add in asparagus. Drain completely, then run cold water over everything until it comes to room temperature. Drain again.
Mix in pesto. Add in burrata pieces, peas, and prosciutto. Toss to combined. For that true pasta salad feel, chill in fridge for 30 minutes before serving!