Combine the shallots, carrot, celery, garlic and parsley in a bowl. Make a bouquet garni by tying the herbs together using cooking string or thread.
Spread a little flour on a plate. Season with salt and freshly ground black pepper. Roll the pork in the flour, shaking off any excess. Heat 4 tablespoons of oil in a casserole. Add the pork, turning to brown it evenly on all sides. Stir in the vegetables and herbs and cook for 2-3 minutes, stirring occasionally. Pour in the white wine and cook until it evaporates, 5-6 minutes.
Add the milk (if you like you can heat it to lukewarm before adding). Cover the pan and lower the heat to barely simmering. Cook the pork over very low heat for 2 hours, turning the meat from time to time.
Remove the pork to a side dish. Remove and discard the bouquet garni, pressing it against the side of the casserole to extract all its flavor. Process the remaining vegetables and sauce using a hand blender. If the sauce is too thin you can thicken it by adding a teaspoon of cornstarch dissolved in 2 tablespoons of cold milk and cooking it in the sauce for 2-3 minutes. If it's too thick, dilute using a little hot milk.
Return the pork to the pan and heat through before slicing the meat and serving with the sauce.