Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil. Place poblano and serrano chiles onto the prepared baking sheet with cut sides down.
Broil until the skin of the chiles has blackened and blistered, 5 to 8 minutes. Place blackened chiles into a resealable plastic bag. Let peppers steam and cool while you prepare the chicken.
Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish with cooking spray.
Heat oil in a large skillet over medium heat. Add chicken; cook until golden and juices run clear, 15 to 20 minutes. Season with salt and pepper. Place chicken in the greased baking dish.
Peel skin off the chiles and discard. Place chiles in a blender with sour cream, water, bouillon, and garlic. Blend very well. Pour the poblano cream over the chicken in the dish. Cover with aluminum foil.
Bake in the preheated oven until sauce thickens, about 45 minutes. Remove from oven and let sit for 5 minutes.
