Steam Broccoli by either putting in Microwave safe dish with lid and a small amount of water, or on stove in a covered sauce pan and small amount of water.
Cook just until soft.
Oil skillet 1/8" in bottom.
Heat, then add 3 TBS Butter.
Add 2 Tbs Flour, chopped Green onion bottoms and ground Pepper.
Cook until Yellow in color, just enough so the flour is not raw.
Add 2 Cans of Chicken Broth.
Stir quickly, using whisk if you have one.
Add Steamed Broccoli and any pan liquids.
Add Green Onion tops, and Simmer 15-20 minutes on Med heat.
This will slightly reduce liquid and impart flavors.
Reduce heat.
Add Colby and American Cheeses.
Cook on low 1 minute.
Add 1 Cup Half and Half slowly, so it will not clump.
Here you must watch temperature, so keep it on low.
Cook 10 minutes.
Add Cornstarch to water and stir.
Pour in 1/2 of cornstarch mixture and stir.
Then pour in 2nd half of mixture and stir.
Turn heat off and stir until thick.