Season steak with salt and pepper.
Heat 1.5 tablespoons olive oil in a large (12 to 14 inch) skillet set over medium-high heat. Cast iron skillet works great with this recipe.
Add sliced steak to the hot oil and cook for 1 to 2 minutes per side. You may want to do this in batches so that the steak browns and crisps up nicely. If the pan is overcrowded, it will steam the steak.
Remove cooked steak from pan and set aside; keep covered.
Drain any liquid from the pan and wipe it down.
Add remaining olive oil and heat it up over medium-high heat.
To the hot oil, add onions, garlic, bell peppers, mushrooms, and Italian Seasoning. Cook for 4 minutes, or until vegetables are soft. Stirring occasionally.
Stir steak back into the skillet and give it a minute to heat through.
Top mixture with cheese slices; lower heat to medium low, and continue to cook until cheese is melted. You can also pop it under the broiler to get a bit of browning on the cheese.
Remove from heat.
Garnish with green onions and parsley.