Preheat the oven to 350 degrees F.
In a large ovenproof skillet heat the vegetable oil over medium-high heat. Season the pork loin all over generously with salt and pepper. Lay the loin, fat side down in the skillet, and cook until golden brown, about 2 minutes. Use tongs to turn the meat, and continue to brown it on all sides, about 2 to 3 minutes per side. Transfer the meat to a plate and set it aside.
Add the onion, carrot, celery, garlic, and herb sprigs to the skillet. Cook, stirring frequently, until the vegetables are softened, about 5 minutes. Remove the skillet from the heat and add the wine. Return the skillet to a high heat and scrape the bottom with a wooden spoon to loosen up any browned bits. Boil the wine until it is reduced by about half. Add the broth and bring to a boil.
Return the loin and any collected juices to the skillet. Transfer the skillet to the oven and roast the loin until an instant-read thermometer inserted into the center of the meat registers between 145 to 150 degrees F., about 40 minutes. (See Cooks Note.)
Transfer the pork to a plate, and cover it loosely with foil. Set it aside in a warm spot while you make a sauce.
Strain the cooking liquid through a fine mesh strainer into a small saucepan; press down on the vegetables with a wooden spoon to extract as much liquid as possible. Discard the solids. Boil the liquid over high heat until reduced by about a third. Reduce the heat to medium-low, whisk in the mustard, and then the bits of butter to enrich the sauce. Season with salt and pepper to taste. Keep warm but do not boil.
Remove the strings from the roast and then slice the loin. Add any collected juices to the sauce. Arrange the meat on a warm platter and season with salt and pepper. Pour the sauce over the meat. Serve with the applesauce on the side.
Cooks Note: Pork cooked this way will be slightly pink. If desired, cook the pork to 160 degrees F., but be aware that this lean cut will not be as moist at the higher temperature.
Remove the apple's stems. Coarsely chop the apples with their skin and seeds. Combine the apples, sugar, and lemon juice with 3 tablespoons of water in a large saucepan. Bring the mixture to a boil over high heat. Cover, and lower the heat to maintain a gentle simmer. Cook until the apples are completely soft, about 20 minutes.
Remove the lid and continue to cook (stir frequently to prevent scorching) until most of the liquid has evaporated, about 10 minutes more. Remove from the heat and cool slightly. Pass the apple mixture through a food mill; discard the peels and seeds. Serve warm or at room temperature. Refrigerate if not using immediately.
Yield: 4 cups
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From Food Network Kitchen