Preheat your oven to 350°F and lightly spray a 9x13 inch baking dish with cooking spray. While the oven heats, mince your garlic and chop your fresh parsley or cilantro, setting them aside. This prep work takes just a few minutes and ensures everything is ready when you need it.
In a bowl, combine the shredded chicken with 1 cup of the green enchilada sauce and 1 cup of mozzarella cheese, mixing until evenly distributed. Warm the flour tortillas slightly (either wrapped in a damp paper towel in the microwave for 30 seconds or briefly over a flame) to make them pliable and prevent cracking. Divide the chicken mixture evenly among the tortillas, placing about 1/4 cup of filling on each one, then roll them tightly and arrange seam-side down in your prepared baking dish. I like to roll them snugly but not so tight that the filling bursts out—this keeps everything neat and ensures even cooking.
Melt 3 tablespoons of butter in a saucepan over medium heat, then add the minced garlic and cook for about 30 seconds until fragrant. Sprinkle the flour over the butter and whisk constantly for 1 minute to create a smooth paste (this is called a roux and prevents lumps in your sauce). Slowly pour in the chicken broth while whisking continuously to incorporate it smoothly, then increase heat to medium-high and keep whisking until the sauce thickens enough to coat the back of a spoon, about 3-4 minutes.
Remove the saucepan from heat and stir in the sour cream and diced green chiles until fully incorporated and smooth. Season generously with salt and black pepper to taste—I recommend starting with 1/2 teaspoon of salt and 1/4 teaspoon of pepper, then adjusting to your preference. The sour cream should be stirred in off the heat to prevent any curdling.
Pour the white sauce evenly over the rolled tortillas in the baking dish, making sure to coat them well. Sprinkle the remaining 1 cup of mozzarella cheese over the top to create a golden, bubbly layer when baked.
Place the baking dish in your preheated 350°F oven and bake for 22-25 minutes, until the sauce is bubbling around the edges and the cheese on top is melted and lightly browned. The enchiladas are done when you see gentle bubbles breaking through the sauce—this indicates the filling is hot throughout and the flavors have married together.
Remove the baking dish from the oven and let it rest for 2-3 minutes before serving. This brief rest allows the sauce to set slightly, making plating easier. Serve each enchilada with a generous spoonful of the white sauce and garnish with the fresh parsley or cilantro for a pop of color and freshness.