Mix the Italian dressing(1Cup), BBQ(1Cup), Worcestershire (1/4-1/2Cup), and garlic (1 tbsp). You may vary this based on flavor preference. Reserve about 1/2 Cup of the mix to the side once done.
You can add the meat to the bowl you mixed the marinade in, or you can use a pan. Either way, get the meat good and coated then cover it and put it into the fridge. How long you want to let it marinade is up to you. I start it the night before then flip the meat ever couple hours the next day until I'm ready to cook. I have however made it with no marinade time and it was still pretty tasty.
Slice up your onion and peppers, keeping them separate. I like to slice them in long narrow slicers.
Put a small amount of olive oil into a skillet or wok (vegetable oil works just fine) and get it heating up. Get the peppers going first as they take the longest, then add in onion, then lastly the mushrooms. Add the reserved marinade.
There are now two way to finish this recipe, with a grill or with an oven.
If you want to grill your meat, go at it. Grill to your preference then top with the vegetables and cheese and serve.
If you want to use your oven, preheat it to 350 degrees, set your meat in a baking pan, cover it with the vegetables and cheese (You can ever poor the marinade the meat was setting in if you want to) and bake it to your preference (If you chose to use chicken breasts please bake until all pinkness has left the meat (Approx. 30 minutes)). Then you're good to serve.