In a Dutch oven or heavy pot, cook bacon over medium until fat is released, 5 minutes. Add onion, carrot, and celery, cook until soft, 6 minutes. Raise heat to medium high; add pork and cook, breaking up meat with wooden spoon, until browned, 7 minutes. Add tomato paste; cook until pork is coated, 4 minutes.
Add wine; cook until reduced by three-fourths. Add 1 cup milk; cook until reduced by half. Add tomato sauce, broth, bay leaf, thyme, 2 1/2 teaspoons salt, and 1/2 teaspoon pepper. Simmer, stirring occasionally, 1 hour. Stir in 1/4 cup milk. Serve sauce over pasta, topped with cheese.
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