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 and set aside. Use FP to chop veg. 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). Cook to 145 degrees. Remove the pork and allow to rest for 15'.
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, puree the sauce until foamy. Adjust the seasoning as needed. Pour over thick slices of roast.