If using fresh broccoli, remove outer leaves and tough parts of stalks. Cut stalks into small bite-size pieces (about 4 cups). In a large saucepan combine the water and chicken bouillon granules; heat to boiling. Add the carrots and fresh or thawed broccoli. Cover and cook about 10 minutes or 'til vegetables are crisp-tender. Drain, reserving the liquid. If necessary, add enough water to the liquid to equal 1/2 cup. Set the liquid and the vegetables aside.
In the same saucepan, melt the butter. Add green onion, cook 'til tender but not brown. Stir in flour, nutmeg, and white pepper. Add the milk and the reserved liquid all at once. Cook and stir 'til thickened and bubbly. Cook and stir 1 to 2 minutes more. Add the Colby cheese and Swiss cheese; cook and stir until cheeses are melted. Stir in the cooked vegetables and sherry; cook and stir 'til heated through. To serve, ladle into soup bowls. Top each serving with additional shredded Colby cheese, if desired.