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1
Place chicken in a large skillet and pour in enough water to cover; add Parmesan cheese and 2 chopped cloves of garlic. Bring water to a boil and cook until chicken is no longer pink in the center, about 28 minutes. Remove skillet from heat, reserving 1/2 cup water mixture from the skillet. Transfer chicken to a work surface and shred using 2 forks.
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2
Combine onion, green chile peppers, and 1 chopped clove of garlic in a pot; add cream cheese and 1 cup Mexican cheese blend. Cook and stir mixture over medium heat until cream cheese is melted, 3 to 4 minutes. Slowly pour the reserved 1/2 cup water mixture from chicken over cream cheese mixture, while continuously stirring until mixture is smooth. Remove pot from heat and stir shredded chicken into cream cheese sauce.
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3
Preheat oven to 350 degrees F (175 degrees C).
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4
Heat oil in a skillet over medium-low heat. Place tortillas in the hot oil, working in batches, until warmed, about 30 seconds per side. Spoon 1 to 2 tablespoons cream cheese-chicken sauce down the center of each warmed tortilla; roll tortilla around filling.
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5
Pour enough green enchilada sauce to cover the bottom of a 9x13-inch baking dish. Arrange filled tortillas in the enchilada sauce. Pour remaining enchilada sauce over filled tortillas.
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6
Mix sour cream and milk together in a bowl until thin enough to pour. Pour sour cream mixture over filled tortillas; top with remaining Mexican cheese blend.
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7
Bake in the preheated oven until heated through and cheese is melted and bubbling, 20 to 25 minutes.
