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Heat the olive oil in a Dutch oven or large skillet over medium heat until shimmering. Add the onion, celery, carrot, and 1 teaspoon of the salt. Cook until the onion is translucent and all the vegetables are softened, 6 to 8 minutes. Add the garlic and tomato paste and cook until the garlic is fragrant, about 30 seconds. (If your skillet isn't big enough to also accommodate the beef at this point, transfer the vegetables to a 6-quart or larger slow cooker and continue cooking the beef by itself.)
Add the beef, breaking it apart with your spoon and cooking until it is just browned. Stir in the thyme, oregano, pepper, nutmeg, and remaining 1 teaspoon salt.
Stir in the milk and bring to a rapid simmer. Continue simmering until the milk has reduced completely and very little liquid remains, about 10 minutes. Stir in the wine and simmer again until reduced completely, about 10 minutes. Using a slotted spoon, transfer the beef mixture to the bowl of a 6-quart or larger slow cooker.
Open the cans of tomatoes and strain through a strainer, reserving the juices. Transfer the tomatoes to the slow cooker, squishing them in with your hands or mashing them against the side of the slow cooker to break them down into small pieces.
Add the bay leaf and stir everything together. The mixture should have a thick, saucy consistency, neither overly soupy or too dry. If it looks dry, mix in a little of the reserved tomato juices until it looks sauce-like. If it looks too soupy, don't worry about it right now — you can let excess liquid evaporate at the end of cooking.
Cover and cook on the LOW setting for 6 to 8 hours. (See below for oven-cooking instructions.) In the last 30 minutes of cooking, check the sauce. If it looks soupy, remove the lid to allow any excess liquid to evaporate and reduce the sauce. If it looks a little dry, stir in some of the reserved tomato juices. The finished sauce should be thick and creamy. Serve over cooked pasta or polenta with Parmesan sprinkled on top, or layer it into a lasagna.