Place hamburger, onion, garlic and salt in a frying pan on medium heat; break up hamburger as it browns; remove beef and set aside; retain 2 tablespoons of fat in the pan; discard any excess.
Add celery and carrot to pan; sauté until vegetables have softened.
Return beef to pan and add wine. Reduce heat to med-low and cook uncovered until wine is evaporated, ~15 minutes. Continue to break up hamburger finely.
Add tomato paste, bay leaf and nutmeg; continue cooking, stirring occasionally, ~5 minutes.
Add chicken broth and milk; reduce heat to low and simmer uncovered, stirring occasionally, 1 hour.
Cook pasta in a large pot of boiling salted water, 2 minutes less than al dente package directions; do not drain; scoop pasta out and transfer to pan with sauce.
Add 1 cup of pasta water and ½ cup Parmesan; increase heat to medium, bring to a bubbly boil, tossing constantly, until pasta is al dente and liquid is slightly thickened, ~2 minutes.
Serve and top with more Parmesan cheese.
