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Heat 2 tablespoons olive oil in a Dutch oven or large pot over medium heat until shimmering. Stir in 1 finely diced small yellow onion, 1 peeled and finely diced small carrot, 1 finely diced small celery stalk, and 3 minced garlic cloves. Cook, stirring occasionally, until the vegetables are softened, 8 to 10 minutes.
Add 1 pound lean ground beef, 1 ½ teaspoons kosher salt, ¼ teaspoon black pepper, and ⅛ teaspoon ground nutmeg. Cook, breaking up the beef into smaller pieces, until cooked through, 5 to 7 minutes.
Stir in 1 cup whole milk and cook, stirring occasionally, until evaporated, 10 to 12 minutes. Stir in 1 cup dry white wine and cook, stirring occasionally, until evaporated, 10 to 12 minutes.
Stir in 1 (28-ounce) can whole peeled tomatoes and their juices, breaking up the tomatoes with your hands into bite-size pieces as you add them to the pot, and 1 cup low-sodium chicken broth. Bring to a simmer. Reduce the heat to low to maintain a very gentle simmer. Simmer, stirring occasionally and breaking up any large pieces of tomato with a wooden spoon, until the sauce is thickened and the flavors meld, about 1 ½ hours.