Place the carrots, onions, celery turnip, apple, and garlic in a food processor and pulse to make a coarse puree.
Place the roasting pan with the pork drippings on the stovetop over medium-high heat. Add a 2-count of olive oil and the vegetable puree. Cook gently for 7 to 8 minutes, until most of the moisture has cooked off. Sprinkle the puree with the flour and cook for 2 more minutes, stirring well to incorporate the flour with the fat in the pan.
Gradually add the chicken broth, stirring as you go to ensure there are no lumps. Bring to a simmer and season well with salt and pepper. Add the Calvados, and continue to simmer for another 20 minutes.
Strain the gravy through a sieve into a saucepan, but don’t use a very fine sieve, as allowing some of the pulp to pass through will help to thicken the sauce. Add a few of the cold butter cubes at a time, and swirl to dissolve them, repeating until all the butter has been incorporated and the sauce is thick, velvety, and rich.
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