In small sauce pot over low heat, melt butter, add flour and stir to make a blond roux paste.
Maintain low heat and stir with wooden spoon to ensure a smooth consistency. Allow to cook for approx ten mins.
Add cold milk to pot and whisk to incorporate. Continue cooking over low heat whisking frequently until sauce has thickened substantially.
Add cubed cheddar cheese and allow to sit still for 5 mins, then continue whisking to evenly distribute cheese.
Whisk until sauce is creamy and smooth and no visible chunks of cheese remain.
In a separate small saute pan, add 2 Tbl Extra Virgin Olive oil add sliced onions and green peppers and saute lightly over med. Heat till softened and translucent.
Add 4 oz cheddar cheese sauce and reserve warm while you cook the beef.
In separate small saute pan, add remaining olive oil season your sliced beef with Salt and Pepper and add to pan. Cook over med hi heat to desired degree of doneness, then add beef to pan with cheese and pepper/onion mix.
Cook over medium heat to allow cheese to thoroughly coat the beef and ensure even distribution throughout. lightly toast your bread roll of choice, add the cooked meat with its sauce and veg.