Pre-heat oven to 350°F.
Place the loin on a cutting board with the fat cap on the board and the small end facing you.
With a very sharp knife, cut the loin lengthwise to within 1/2 inch of bottom of pork, cutting to, but not through, the other side.
Open the cut pork like a book. Repeat process with each half, being careful to cut to within 1/2 inch of the bottom of the pork but not through.
Top butterflied pork with plastic wrap; gently pound with a meat mallet or rolling pin to an even 1/2-inch thickness; remove plastic wrap, and discard.
Sprinkle 1-1/2 teaspoons salt over pork; spread evenly with pesto.
Top pesto with prosciutto; sprinkle evenly with Parmesan.
Roll meat back into a tight spiral, and, using butcher’s twine, tie roll in 6 places.
Season on all sides with pepper and remaining 1 teaspoon salt.
Heat an oven-safe skillet over medium-high.
Rub roast with olive oil and sear, starting fat side down and turning roast occasionally, until roast is evenly browned; 10 to 12 minutes.
Place skillet in pre-heated oven and roast until a meat thermometer inserted in center reads 135°F; 45 to 50 minutes.
Transfer to a cutting board and let pork rest, lightly tented with aluminum foil, at least 15 minutes.
To serve, remove strings, and slice as desired.
