Finely chop the onion, carrot, garlic, and celery.
Heat the oil and butter in a saucepan over medium heat. Add the vegetables, then cook until softened, 5-6 min, with some stirring. Add the chicken, then salt and pepper to taste. Cook, stirring frequently and breaking up the meat with a spoon until it loses its pink colour and starts browning, about 7-8 min.
Raise the heat to high, then add the milk. Cook, stirring frequently, until the liquid has evaporated, about 3 min. Add the wine (optional), then cook, stirring frequently, until the wine has evaporated, about 3 min.
Stir in the diced tomatoes, tomato paste, and oregano, then cover and simmer
gently over low heat for at least 1 h. Stir occasionally and add some water as needed to prevent the sauce from becoming too dry. Season with additional salt and pepper. It is important to simmer all the ingredients until the sauce is thick and the chicken very tender. (If you are using a pressure cooker, the cooking time is reduced to 15 min from the time it starts to spatter).
The sauce can be stored up to 1 week in the refrigerator or up to 2 months in the freezer.
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