Cook the bacon. Heat the olive oil and some of the butter in a large skillet or Dutch oven over medium heat. Add the chopped bacon and cook until lightly crisp and golden.
Brown the pork. Pat the pork dry with paper towels, then add it to the pan. Brown the pieces on all sides over medium heat without cooking them all the way through.
Add the flour. Sprinkle the flour over the pork and stir gently for about 2 minutes, until it coats the meat and loses its raw taste.
Add the liquids. Slowly pour in the white wine, followed by the water or stock. Stir gently, loosening any browned bits from the bottom of the pan.
Add the vegetables. Press the cloves into the onions, then add them to the pan with the carrots, thyme, bay leaves, salt, and black pepper. Bring to a gentle simmer.
Simmer the pork. Cover the pan, reduce the heat to low, and simmer gently for about 40 minutes, checking occasionally. The sauce should barely bubble. Add a splash of stock if needed.
Cook the mushrooms. Toward the end of cooking, sauté the sliced mushrooms in a separate skillet with the remaining butter until golden.
Finish the sauce. Temporarily remove the pork and clove-studded onions from the pan. Stir in the heavy cream, then return the pork and add the golden mushrooms.
Simmer gently. Cook over low heat for another 10 to 15 minutes, stirring occasionally, until the sauce becomes creamy and slightly thickened. Avoid boiling.
Finish and serve. Remove the bay leaves and whole cloves, sprinkle with fresh parsley, and serve warm with mashed potatoes, rice, or noodles.