Heat the oven to 400 degrees F. Butterfly the pork loin by making a horizontal slit in the loin, cutting almost through to the other side. Open the meat flat, like a book, so it's an even thickness. Mince the garlic, sprinkle the salt over it on the cutting board, and repeatedly scrape the flat side of a chef's knife over the garlic until it has a paste-like consistency. Scrape the garlic into a small bowl and mix in the rosemary, pepper, and 2 tablespoons of the oil. Spread two-thirds of this paste on the inside of the pork and then roll and fold the stuffed loin over itself so that it forms a tight cylinder. Using kitchen twine, tie the meat at 1 1/2 inch intervals. Reserve the remaining paste.

Heat the remaining 2 tablespoons oil in a Dutch oven over medium-high heat and brown the meat thoroughly on all sides, about 2 minutes on each side. Pour the milk into the pan and then spread the remaining rosemary-garlic paste on top of the pork. Cover and roast in the oven, basting occasionally with the pan juices, until an instant-read thermometer inserted in the center of the meat registers 145 degrees F, 30 to 40 minutes. If the sauce reduces rapidly during cooking, add more milk.

Transfer the pork to a carving board, cover it loosely with foil, and let it rest for 5 to 10 minutes. Whisk the sauce vigorously to break up the clumps of milk solids and smooth the texture. If the sauce looks very watery, simmer it on the stovetop until it's reduced to about 3/4 cup. Taste and adjust the seasonings. To serve, carve the pork into thick slices (discarding the strings) and arrange overlapping slices on a platter. Spoon the sauce over the pork and decorate with the rosemary sprigs.