Preheat oven to 350 degrees. Cook chopped broccoli then set aside. Melt butter in saucepan, stir in flour and cook over high heat for 2 minutes. Remove from heat. Add milk, whisk vigorously. Return to heat, stirring until thick and smooth, continue to stir while adding cheese and spices. Remove from heat and add beaten egg yolks little by little -- do not boil or mixture will curdle. Add drained broccoli and set the mixture aside. Beat the cream of tartar with the egg whites with until they are stiff. Fold in 1/3 of the whites to the broccoli mixture. Fold in the remaining egg whites.
Pour mixture into an 8 cup buttered souffle dish and bake in the preheated 350 degree oven for 45 minutes.