Step 1

Preheat oven to 350°F. Lightly coat a 9-by-13-inch baking dish with cooking spray.

Step 2

Heat 1 tablespoon oil in a large skillet over medium-high heat. Add onions, celery, mushrooms and 1/4 teaspoon salt; cook, stirring often, until the vegetables are softened and the mushrooms are browned, 6 to 8 minutes. Add kale and garlic; cook, stirring frequently, until the kale is just softened, about 1 minute. Stir in rice and chicken; transfer to the prepared baking dish.

Step 3

Heat butter and the remaining 2 tablespoons oil in the skillet over medium heat until the butter is melted. Whisk in flour until smooth; cook, stirring frequently, until lightly golden, about 1 to 2 minutes. Gradually whisk in broth; simmer until just thickened, 3 to 4 minutes. Remove from heat. Whisk in sour cream, thyme, parsley and the remaining 1/4 teaspoon salt; pour over the chicken and rice. Stir to combine, then top with crushed crackers.

Step 4

Bake until bubbling on the edges, about 30 minutes. Let stand for 10 minutes before serving.