To make the rub, put the garlic in the food processor and pulse to get it started. Add the oregano, parsley, thyme, sage, anchovies, and giardiniera, salt and pepper, lemon zest and juice. Pulse together. Add the oil and pulse some more until it forms a paste.
To butterfly your pork, place the meat fat cap side down on your cutting board. Using a super sharp knife, slice the pork lengthwise parallel to the counter, starting about an inch above the fat cap. Slice along the meat so that it unrolls as you cut along. Try to cut it so that the meat touching the counter as it unrolls is uniformly thick. Make smaller slashes in any thicker spots.
Season the pork with salt and pepper. Rub the herb-anchovy mixture all over the inside of the pork. Roll it up and, using butcher's twine, tie it very tightly about every two inches. Score any visible fat in a crosshatch pattern and season the outside with salt and pepper. Place the pork onto a roasting rack in a roasting pan, fat cap side facing up. Pour 1 cup of water in the bottom of the pan to keep the drippings from burning.
Roast until super fork tender and "pullable" and the internal temp registers 200 degrees F, about 4 1/2 to 5 hours. Take out and let rest for at least 20 minutes.
Pour the liquid and renderings from the roasting pan into a small saucepan and simmer over medium heat until slightly reduced. Season to taste.
Either pull or carve the roast—your preference. I like to carve it so you can see the stuffed interior. Place on a platter, garnish with plenty of parsley, and serve with the pan sauce and fresh lemon wedges.