Step 1

Combine mushrooms and water in a medium heatproof bowl. Set aside.

Step 2

Heat oil in a large pot over medium-high heat. Add pork and cook, breaking up the meat with a wooden spoon, until no longer pink, 4 to 5 minutes. Add beef and veal; cook, breaking up the meat, until no longer pink, 5 to 7 minutes. Add celery, carrot, onion, garlic and parsley; cook, stirring often, until the vegetables are soft, about 10 minutes more.

Step 3

Strain the mushrooms, reserving the soaking liquid. Mince them and add to the pot along with the soaking liquid. Add tomatoes and their juices. Bring to a boil. Reduce heat to maintain a simmer, partially cover and cook, stirring occasionally, until thickened, 2 to 2 1/2 hours.

Step 4

Remove the sauce from the heat and stir in butter and salt.