Pulse onion in a food processor until diced but not mushy. Transfer to a bowl. Repeat with celery and carrot. Pulse portobello mushrooms to the consistency of ground beef.
Coat the bottom of a large pot with oil; heat over low heat. Cook and stir onion in the oil until soft but not browned, about 5 minutes. Stir in celery and carrot; cook until slightly softened, about 5 minutes. Add portobello mushrooms; cook about 1 minute. Season with salt.
Pour wine into the pot. Increase heat to medium-high; stir with a flat wooden spoon until bottom of the pot looks almost dry, 3 to 5 minutes. Add milk and nutmeg. Reduce heat to medium; cook and stir until bottom of the pot is almost dry, 3 to 5 minutes.
Pour tomato juice from the cans into the pot. Pulse tomatoes in the food processor until coarsely chopped; stir into the pot. Bring to a boil; reduce heat to low and simmer until flavors combine, 3 to 4 hours. Thin sauce with water if it appears too thick.