Preheat the oven to 350 degrees. Spray a 9x13 baking dish with non-stick cooking spray.
In a large saucepan, melt the butter to sizzling over medium heat. Add the green onions and garlic. Saute' for about 30 seconds.
Stir in the cream of chicken soup, cream of mushroom soup, sour cream and diced green chiles. You don't have to add the whole can of chiles if you don't want to. Personnally I only use half a can because I'm not a big fan of spicy foods, but I know others like a little more heat than I do. So it's up to you.
Spoon out 1 cup of this sauce and set aside.
Add the chicken and 1 cup of shredded cheese to the sauce in the pan. Mix well.
Lay out the tortillas across your countertop and divide the chicken/cheese filling amongst them. Roll the tortillas up and place them seam down in the prepared baking dish.
Whisk the milk into the cup of sauce that you set aside. Pour over the top of the chicken enchiladas. Top with the remaining cup of cheese.
Bake at 350 degrees for 30-40 minutes.