Preheat the oven to 350 degrees F. Combine the raisins, prunes and apricots in a small bowl; pour in the brandy. Cover with plastic wrap and microwave until hot, about 2 minutes. Set aside until the dried fruit is plump, at least 10 minutes.
Meanwhile, heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the shallot and apple and cook until softened, 3 to 4 minutes. Add the garlic, parsley, sage, 1 teaspoon rosemary, 1/2 teaspoon salt and a few grinds of pepper. Cook until the garlic is softened, about 1 minute. Add the dried fruit?brandy mixture and cook until the skillet is dry, 1 to 2 minutes. Add the chicken broth and simmer until the mixture is very soft and the skillet is almost dry, about 5 minutes. Let cool completely.
Push the handle of a wooden spoon into the center of one end of the pork roast; work the handle through the length of the roast to create a tunnel, widening the tunnel with your fingers or a small paring knife until about 1 1/2 inches wide.
Stuff the dried fruit mixture into the tunnel, firmly pressing to make sure it?s packed into the pork roast. Rub the outside of the pork roast with the remaining 1 tablespoon olive oil and sprinkle with the remaining 1 tablespoon rosemary, 1 teaspoon salt and 1/2 teaspoon pepper. If the pork has a skinny flap that runs along one side, tuck it under and tie kitchen twine around the pork in a few spots.
Set a rack in a large roasting pan. Place the pork on the rack and roast until golden brown and a thermometer inserted into the center registers 140 degrees F, 1 hour 15 minutes to 1 1/2 hours. Let the pork rest at least 20 minutes before slicing.