How to Make It
Combine basil, tarragon, dill, chives, scallions, thyme, horseradish, garlic, and lemon zest in a blender or food processor. With processor running, drizzle in oil through food chute. Process until mostly smooth.
Preheat 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. Sear, starting fat side down and turning roast occasionally, until roast is evenly browned, 10 to 12 minutes. Place skillet in preheated oven and roast until a meat thermometer inserted in center reads 135°F, 45 to 50 minutes. Transfer to a cutting board. Let pork rest, lightly tented with aluminum foil, at least 15 minutes. To serve, remove strings, and slice as desired.