1. Preheat the oven to 350=B0. Melt 1 tablespoon of the butter in a = large skillet. Add the poblanos and onion and cook over moderate heat, = stirring, until softened, about 10 minutes.

2. Meanwhile, melt the remaining 1 tablespoon butter in a large heavy = skillet. Season the chicken breasts with salt and pepper and add them to = the skillet. Cook over moderately high heat until browned, about 5 = minutes per side. Arrange the chicken in a baking dish large enough to = hold them in a single layer.

3. Transfer the cooked poblano mixture to a blender with the sour cream = and milk; puree until smooth. Season with salt and pepper. Pour the = sauce over the chicken and sprinkle the cheese on top. Bake for about 25 = minutes, until the sauce is bubbling and the chicken is cooked through.