Step 1

Preheat oven to 350 degrees F. Heat oil in a medium saucepan over medium-high heat. 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.

Step 2

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. Remove from heat. Whisk in sour cream.

Step 3

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.

Step 4

Bake until the cheese is lightly browned and the edges are bubbly, 20 to 25 minutes. Sprinkle with cilantro and serve.