In the first pan put enough oil to lubricate and brown the potatoes O'Brien on med to high heat, stirring occasionally (per package directions, yours may vary).
In the second pan brown the breakfast sausage.
In a bowl beat the eggs along with the milk and set aside.
Just as the sausage finishes browning, toss in the ham with it to put a little color on it (it's diced and pre-cooked generally, so this should go quick).
Right after you add the ham to the sausage, add the green onions, bell peppers, and mushrooms to the potatoes O'Brien in the first pan, and sauté the potatoes and veggies together for about 5 minutes.
Once the ham has browned slightly, drain the fat, and add the sausage and ham to the first pan with the potatoes and veggies and stir the mixture together, then stir occasionally.
After dumping the sausage and ham, put the pan back on the heat and use it to scramble your eggs (the grease from the sausage will do a wonderful job lubricating the pan and imparting a little flavor to the eggs).
Once the eggs are scrambled fold them into the first pan, do not over mix, or you will turn the texture to mush.
Top the mixture with cheese, and gently stir to mix in the cheese,.