Preheat your oven to 350°F and grease a 9x13-inch baking dish.
In a medium bowl, mix together the shredded chicken, softened cream cheese, garlic powder, and half of the shredded cheese (about 1 cup).
Evenly divide and stuff the mixture into the flour tortillas, then roll them up and place them seam-side down in the prepared baking dish.
In a saucepan over medium heat, melt the butter.
Stir in the flour and taco seasoning to form a roux.
Gradually whisk in the chicken broth until the sauce is smooth and begins to warm through.
Add 1/2 cup of shredded cheese and whisk until melted and fully combined.
Stir in the sour cream and diced green chiles, whisking just until the sour cream dissolves (do not let the sauce boil).
Pour the warm sauce evenly over the stuffed tortillas in the dish.
Sprinkle the remaining shredded cheese on top.
Bake uncovered for 22–25 minutes until bubbly.
Switch the oven to broil for 2–3 minutes, just until the cheese begins to brown.
Serve warm, optionally topped with hot sauce and sides like refried beans or Spanish rice.