Preheat the oven to 425°F. Spray a 9×13-inch baking dish with cooking spray and set aside.
In a pyrex measuring cup, add 2 cups of water and 2 chicken bouillon cubes. Microwave on high for two minutes, then set aside.
In a large skillet over medium heat, add 1 tablespoon of olive oil and the ½ yellow onion diced finely. Cook for 5 to 7 minutes until the onion is soft and translucent.
Add 2 teaspoons of minced garlic and cook for an additional 1 to 2 minutes. Stir in 3 cups of shredded chicken and season with ½ teaspoon of salt and ½ teaspoon of pepper.
Assemble the tortillas by evenly splitting the chicken mixture between 8 large flour tortillas. Sprinkle 2 cups of shredded Monterey Jack cheese on top of each filling.
In a saucepan over medium heat, melt 3 tablespoons of butter. Add 3 tablespoons of flour and whisk together until smooth.
Slowly add the chicken broth, whisking constantly until smooth and thickened, about 5 minutes.
Stir in 1 cup of sour cream, ½ teaspoon of salt, ¼ teaspoon of pepper, 4 ounces of green chilies, and ½ cup of Monterey Jack cheese until combined.
Pour the sauce over the enchiladas in the baking dish and top with 1 cup of Mexican blend cheese. Bake for 20 minutes until the cheese is melted and bubbly.