Preheat oven to 400 F.
In a large frying pan or skillet, sauté onions in the olive oil, add beef (or turkey if you prefer) and brown well. Drain off excess fat, if any.
Add drained chilies, tomato soup (do not dilute); oregano, salt, and pepper to taste. Heat through. Set aside.
In a separate bowl, mix the Bisquick and milk (or Master Mix and water) into a dough. Roll out to the size of the skillet in which you've prepared the meat mixture. Place this on top of the meat mixture.
Move the skillet into the oven for 15-20 minutes, or until the biscuit top is lightly browned. (If your skillet has a wood handle, wrap the handle with aluminum foil).
Remove from the oven and allow to cool for 10 minutes.
Carefully place a heatproof platter or plate on top of the skillet. Carefully, holding on to both the skillet and the platter, turn it over so that the entire contents of the skillet are upside down on the platter or plate.
Top with grated cheese, return to oven until cheese is melted. Don't take your eyes off of it as this will happen quickly!
Remove from oven. Allow to cool for 5 minutes. Cut into pieces and serve, pie fashion.