Add onion and poblano; cook, stirring occasionally, until softened, 4 to 5 minutes.
Add cumin and cayenne; cook, stirring constantly, for 30 seconds.
Whisk flour and 1/4 cup broth in a small bowl; set aside.
Add the remaining 1 3/4 cups broth to the pan and bring to a boil over medium-high heat.
Whisk in the flour mixture and simmer, whisking often, until thickened, 2 to 3 minutes.
Whisk in sour cream.
Coat a 7-by-11-inch (2-quart) baking dish with cooking spray.
Combine chicken, 1/2 cup of the white sauce and 1/4 cup cheese in a medium bowl.
Spoon 1/4 cup of the chicken mixture down the center of each tortilla.
Roll up and place, seam-side down, in the prepared baking dish.
Pour the remaining white sauce over the enchiladas and sprinkle evenly with the remaining 1/2 cup cheese.
Bake until the cheese is lightly browned and the edges are bubbly, 20 to 25 minutes.
Sprinkle with cilantro and serve.
- Daily Values (DVs) are the recommended amounts of nutrients to consume each day.
(-) Information is not currently available for this nutrient.