Tie parsley, thyme, and bay leaf together to make a bouquet garni.
Season the pork with salt and pepper.
Heat the oil in a Dutch oven over medium-high heat, and add the butter. Brown the roast on all sides (6 to 7 minutes total).
Remove roast from pan and set aside. Add onion, carrot, leak, and garlic to pan and stir over high heat until soft (10 minutes or so).
Add the flour stirring constantly and cook for 2 minutes, then slowly add the milk and bouquet garni and bring to a boil.
Let simmer for 5 minutes then add the roast. Cover and cook over low heat for 1 hour making sure to rotate the pork every 15-20 minutes to prevent scorching. Remove the pork and let rest for 10-15 minutes.
While the pork is resting, remove the bouquet garni, and strain the cooking liquid into a small pot and bring to a boil. Using a hand blender or food processor, puree the sauce until foamy, and adjust seasoning to taste with salt & pepper.