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COOK THE PORK: Season the pork with salt and pepper. Heat the oil in the Dutch oven. When the oil is hot, add the butter. Brown the roast on all sides, 6 to 7 minutes total. Remove the roast from the pan and set aside on the large plate. Add the onion, carrot, leek, and garlic and stir over high heat until soft and caramelized, about 10 minutes. Stirring constantly, add the flour and cook for 2 minutes, then add the milk and the bouquet garni. Bring to a boil and cook over high heat for 5 minutes. Add the pork and any juices that have collected on the plate. Reduce the heat to a simmer. Cover and cook over low heat for 1 hour, making sure to periodically rotate the pork (the sugars in the milk can cause sticking and scorching). Remove the pork and allow to rest for 15 minutes.
FINISH THE SAUCE AND SERVE: Remove and discard the bouquet garni. Strain the cooking liquid into a small pot and bring to a boil. Using a hand blender, purée the sauce until foamy. Adjust the seasoning as needed. Carve the pork and arrange on a serving platter. Spoon the sauce over and around and serve immediately.