In 8-quart pot, bring stock to boil. While stock heats, coarsely chop broccoli. Do not use last 3 inches of stalks. Add broccoli to boiling stock; simmer 15 minutes.

Meanwhile, in small saucepan, melt butter, add flour and cook, whisking, 2 to 3 minutes to make a roux. Add cream to soup, then slowly add roux to soup, mixing briskly with wire whip. Add enough roux so that soup coats back of spoon. When soup is thickened add cheese and blend until melted. Stir regularly so cheese does not burn on bottom of pot. Keep hot until ready to serve. Makes about 10 servings.