Lay out each flour tortilla and add a portion of the chicken mixture. Sprinkle with shredded cheddar and Monterey Jack cheese.
Roll each tortilla tightly and place seam-side down in a greased 9×13-inch baking dish.
Prepare the Creamy Sauce:
In a saucepan over medium heat, whisk together the sour cream, heavy cream, chicken broth, garlic powder, smoked paprika, and cayenne pepper (if using). Season with salt to taste.
Cook the sauce until it is smooth and heated through, about 5-7 minutes.
