Using a knife, score the fat on top of pork loin.
To butterfly roast, place roast fat-side up on cutting board. Starting about 1 inch up from cutting board, cut horizontally down, stopping about ½ inch before the edge.
Now, cut into thicker half of roast, again, starting about 1 inch from cutting board and stopping about ½ inch before edge.
Add basil, walnuts and garlic into a food processor and purée until smooth.
Slowly pour in ⅓ cup olive oil and process until oil is emulsified and pesto holds together. Add parmesan and pulse until combined.
Open butterflied roast and layer prosciutto over it. Spread pesto mixture evenly over the prosciutto.
Roll meat tightly and tie with kitchen twine at 1-2 inch intervals.
Roast can be wrapped tightly with plastic wrap and refrigerated for 24 hours at this point.
Coat the outside of the roast with 1 tbsp olive oil and season with salt and pepper.
If cooking in the oven, preheat to 350ºF. Place pork in a roasting pan and roast 40 minutes, or until meat thermometer reaches 140ºF, approximately 30 minutes.
If grilling, preheat grill with all burners on high for 10 minutes, with lid closed. Scrape and oil cooking grate. Place roast on grill and grill until browned all over, about 12 minutes.
For charcoal grills, place roast directly over coals. Leave primary burner on high and shut off other burner(s). and roast fat-side up on cooler side of the grill. Cook covered until meat thermometer internal temperature reads 140ºF, about 35 minutes.
Transfer pork to cutting board, tent with foil, and let rest 15 minutes. Allow the pork's internal temperature to rise and reach 150ºF. Remove twine, slice and serve.
