Cook fusilli in water with the tablespoon salt. Add broccoli for the final 3 minutes, then reserve 1 cup cooking water and drain when the pasta is just tender and broccoli is bright green.
Meanwhile, melt butter in a large skillet over low heat and stir garlic for 30 seconds. Add cream, milk, sauce salt and pepper and simmer gently for 2 minutes.
Remove the skillet from heat and stir in Parmesan gradually until smooth. Add pasta and broccoli with 1/4 cup reserved water.
Fold gently until the sauce coats the spirals and florets, adding more cooking water by the tablespoon if needed. Serve promptly.