FOR FRIED VERSION: In a large, cast iron OR heavy-bottom skillet, pour in enough vegetable oil to fill it 2 inches full of oil. Heat oil over low heat. (This will be the oil you fry the chimichangas in. The oil needs to slowly reach about 375 degrees F.)
FOR BAKED VERSION: Preheat oven to 375 degrees F.
In a separate large skillet, heat 2 tablespoons of vegetable oil over medium-high heat. Add in the diced onion and cook until slightly softened. Add in garlic, chili powder, oregano and cumin.Stir and cook until fragrant, about 1 minute. Add the shredded, cooked chicken. Season with salt and pepper. Stir in the green chilies and continue to stir and cook mixture for another 5 minutes, or until thoroughly heated. Set aside. Warm tortillas in the microwave. On each tortilla, add about 1/2 cup of the chicken mixture into the center. Top with 3 tablespoons of the shredded Monterey jack cheese.Fold sides over the mixture, then fold bottom over the sides and roll up. Place folded chimichangas, seam side down on a large plate/platter, and repeat with remaining tortillas. FOR FRIED VERSION: Using tongs, lower one chimichanga at a time, into the hot oil, seam side down. (*It is helpful to hold them with the tongs while they are in the oil to keep them from opening.)Carefully fry until golden brown on both sides. This only should take a minute or two.
Place fried chimichangas onto a paper towel lined plate to soak up grease. Serve warm with your favorite toppings!
FOR BAKED VERSION: Place the wrapped chimichangas onto a lightly greased baking sheet. Spray the tops with non-stick spray. Bake in preheated oven for 20 to 30 minutes, or until golden brown.