Start by shredding the cooked chicken into bite-sized pieces, then set aside.
In a large skillet, melt the butter over medium heat and add minced garlic, cooking until fragrant and golden, about 1 minute.
Add the flour to the butter and garlic, whisking continuously to create a smooth roux, cooking for about 1 minute to eliminate raw flour taste.
Gradually pour in the chicken broth, whisking constantly until the sauce begins to thicken and is smooth.
Stir in the sour cream, paprika, salt, and pepper, cooking just until warmed through and the sauce is creamy.
Fold the shredded chicken into the sauce, coating it evenly and allowing it to heat through for a few minutes.
Preheat your oven to 375°F (190°C). Lightly grease a shallow baking dish with butter or non-stick spray.
Warm the tortillas slightly to make them more flexible, then spoon about 2-3 tablespoons of the chicken mixture onto each tortilla and roll tightly.
Arrange the filled tortillas seam-side down in the prepared baking dish, snugly fitting them side by side.
Pour the remaining sauce evenly over the layered enchiladas, then sprinkle generously with shredded cheese.
Bake uncovered for 20-25 minutes, until the cheese is bubbly and golden brown around the edges.
Remove from the oven and let rest for a few minutes before serving. Enjoy the creamy, cheesy layers with a side of your favorite vegetables or rice.