Cut off and discard tough broccoli ends.
Set aside a few whole flowerets for garnish; finely chop remaining broccoli.
In a 5- to 6-quart pan, bring 3 quarts water to a boil over high heat.
Add pasta; cook, uncovered, until tender to bite, about 3 minutes.
Drain pasta, rinse with cold water, and drain again.
While water is heating, melt butter in a 12- to 14-inch frying pan over medium-high heat; add broccoli (including reserved flowerets) and 1/3 cup water.
Cover and cook until broccoli is tender when pierced, about 5 minutes; set flowerets aside.
Add cream and nutmeg to pan; bring to a boil, then add cooked, drained pasta.
Cook, stirring, until mixture is hot and cream clings to pasta.
Remove from heat.
Sprinkle with 1 1/4 cups of the cheese; mix with 2 forks.
Put pasta onto a hot platter and top with broccoli flowerets and 3 to 4 tablespoons of the remaining cheese.