Combine sage, garlic, rosemary, salt and pepper in a small bowl. Set aside.

Preheat oven to 450 degrees F.

You're going to double butterfly the tenderloins, so they can be flattened, stuffed and rolled. To do that, you'll make two long horizontal cuts, one on each side, dividing the tenderloin in thirds without cutting all the way through. Working with one tenderloin at a time, lay it on a cutting board. Holding the knife blade flat, so it's parallel to the board, make a lengthwise cut into the side of the tenderloin one-third of the way down from the top, stopping short of the opposite edge so that the flaps remain attached. Rotate the tenderloin 180 degrees . Still holding the knife parallel to the cutting board, make a lengthwise cut into the side opposite the original cut, starting two-thirds of the way down from the top of the tenderloin and taking care not to cut all the way through. Open up the 2 cuts so you have a large rectangle of meat. Use the heel of your hand to gently flatten the meat to about 1/2 inch thick.

Cover each butterflied tenderloin with 2 of the ham slices, then spread 1/2 cup Parmigiano-Reggiano over the ham, leaving a 1-inch border. Starting with a long side, roll up each tenderloin so the stuffing is in a spiral pattern; then tie the roasts at 2-inch intervals with kitchen string.

Lightly brush the roasts all over with 1 1/2 teaspoons oil then rub with the reserved herb mixture. Heat the remaining 1 1/2 teaspoons oil in a large, heavy, ovenproof skillet over medium-high heat. Add the roasts, bending to fit if necessary, and cook, turning often, until the outsides are browned, 3 to 5 minutes total.

Transfer the pan to the oven and roast, checking often, until the internal temperature reaches 145 degrees F , 15 to 20 minutes. Transfer to a cutting board, tent with foil and let rest for 5 minutes. To serve, remove the string and cut the pork into 1-inch-thick slices.

MAKE AHEAD TIP: Equipment: Kitchen string