Warm the olive oil and butter in a large skillet or Dutch oven over medium heat. Add the chopped bacon and cook until lightly crisp and golden, letting the fat render and flavor the pan.
Pat the pork dry with paper towels, then add it to the pan. Let the pieces brown on all sides over medium heat. This step builds flavor, the pork does not need to be fully cooked yet.
Sprinkle the flour over the pork and stir gently for about 2 minutes, just until the flour coats the meat and loses its raw taste.
Slowly pour in the white wine, followed by the water or stock, stirring to loosen any browned bits from the bottom of the pan.
Add the carrots, onions studded with cloves, thyme, bay leaves, salt, and black pepper. Bring everything to a gentle simmer.
Cover the pan, lower the heat, and let the stew simmer slowly for about 90 minutes, until the pork is tender and the flavors are well developed.
Toward the end of cooking, sauté the mushrooms in a small skillet with a little butter until golden.
Remove the pork and onions from the pot. Stir the heavy cream into the sauce, then return the pork and add the mushrooms.
Let everything simmer gently for another 10 to 15 minutes, just until the sauce becomes creamy and slightly thickened.
Remove the bay leaves, sprinkle with fresh parsley, and serve warm with mashed potatoes, rice, or noodles.