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1. Process carrot, celery and onion in food processor until finely chopped, about ten 1-second pulses, scraping down bowl as necessary; transfer mixture to small bowl. Wipe out bowl and process tomatoes and juice until finely chopped.
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2. Heat butter in heavy-bottomed Dutch oven over medium heat until foaming; add carrot, celery and onion and cook, stirring occasionally, until softened but not browned, about 4 minutes. Add ground meats and cook, breaking meat into 1-inch pieces with wooden spoon, about 1 minute.
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3. Add milk and stir, breaking meat into 1/2-inch pieces, until almost all liquid has evaporated, 20 to 30 minutes. Break up any remaining clumps of meat (no large pieces should remain).
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4. Add wine and bring to simmer; cook, stirring occasionally, until liquid has evaporated, 20 to 30 minutes.
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5. Stir in garlic and tomato paste and combine. (I usually add some herbs at this point such as fresh basil and parsley or some prepared pesto.)
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6. Add chopped tomatoes, salt and pepper. Bring to simmer, then reduce heat to medium-low and cook until sauce is slightly thickened, about 15 minutes. You should have about 6 cups meat sauce, and it will be thinner than you expect.
