Prepare the Pork: Begin by seasoning the pork loin roast with salt and pepper. In a Dutch oven, heat olive oil over medium-high heat. Once the oil is hot, add the butter and allow it to melt. Brown the roast on all sides for about 6 to 7 minutes, ensuring it is evenly seared. Remove the roast from the pan and set it aside on a plate.

Cook the Vegetables: In the same Dutch oven, add the chopped onion, carrot, leek, and garlic. Stir these ingredients over high heat until they soften and begin to caramelize, which should take approximately 10 minutes. Constantly stir to avoid burning.

Prepare the Sauce: Sprinkle the flour over the softened vegetables and stir for 2 minutes to cook the flour. Gradually add the whole milk, followed by the parsley, thyme, and bay leaf. Bring the mixture to a boil and cook over high heat for 5 minutes, allowing the sauce to thicken slightly.

Simmer the Pork: Return the browned pork to the pot, along with any juices that have accumulated on the plate. Reduce the heat to low and cover the pot. Let it simmer gently for about 1 hour, periodically rotating the pork to prevent it from sticking or scorching due to the sugars in the milk.

Finish the Dish: After 1 hour, remove the pork from the pot and let it rest for 15 minutes. Discard the bay leaf from the sauce. Using an immersion blender, purée the sauce until it becomes foamy. Taste and adjust seasoning with salt and pepper as necessary.