Preheat the oven 425 degrees F. Combine the mayonnaise and pesto in a bowl; cover and store in the fridge. Lay the slices of prosciutto on a work surface, slightly overlapping them. Season the beef with pepper (the prosciutto will add the salt). Set in the middle of the prosciutto; wrap the slices around the beef. Set the beef in a small, parchment-lined roasting pan. Roast 30 minutes; it should be cooked medium rare. Cook longer if you like it more well-done. When the beef is cooked, let it rest 5-10 minutes, and then thinly slice. Serve the pesto-flavoured mayonnaise alongside for dipping.