Preheat the oven to 450 degrees
Put the potatoes, shallots, carrots, parsnips, and garlic in a large heavy roasting pan, sprinkle with the smoked paprika, and toss with 3 tablespoons of the olive oil to coat. Season with salt and pepper. Spread the vegetables evenly over the bottom of the pan. Place 2 of the rosemary sprigs on top.
Finely chop enough of the remaining rosemary sprigs to equal 2 teaspoons. In a small bowl combine 1 tablespoon of salt and the chopped rosemary. Rub the mixture with your fingertips for about one minute, or until fragrant.
I SKIPPED THIS AND STILL DELICIOUS Using a sharp knife, score the top of the roast by cutting shallow slices (about 1/4 inch deep) at one inch intervals, cutting into the fat but not into the flesh. Rub the pork all over with the remaining one (1) tablespoon of olive oil. I SKIPPED THIS AND STILL DELICIOUS Rub the rosemary and salt all over the pork, working it into the score marks. If desired, tie the pork crosswise with the chicken twine in three or four places to help maintain the shape while roasting.
Place the pork fat side up on top of the bed of vegetables. Roast for about 40 minutes, or until the pork is golden brown and an instant-read thermometer entered into the center reads 125 degrees. Transfer the pork to a serving platter. Tent with aluminum foil and let rest for 10 minutes before slicing (the pork will continue to cook as it rests).
Meanwhile, stir the vegetables in the pan and continue to cook them for about 10 minutes, or until golden brown. Transfer the vegetables to the platter with the pork.
I SKIPPED THIS Add the broth to the hot roasting pan and bring to a boil over medium-high heat, stirring with a wooden spoon to scrape the brown bits in the bottom of the pan. Season with salt and pepper. Pour the pan juices into the sauce boat.
Untie the pork if necessary. Slice the pork and serve it with the roasted vegetables and pan juices.