How to Make It
Preheat the oven to 375°. Lightly butter an 8-inch square baking dish.
In a medium skillet, melt 1 tablespoon of the butter over moderate heat. Add the onions, season with salt and pepper and cook, stirring occasionally, until are translucent, about 10 minutes. Add the sliced mushrooms and cook, stirring occasionally, until the mushrooms are softened and browned, about 8 minutes. Scrape the vegetables into a large bowl and return the skillet to the stove.
In a small saucepan, combine the chicken broth and the milk and warm over moderately low heat until just simmering, about 6 minutes.
Meanwhile, in the skillet, melt 4 tablespoons of the butter over moderate heat, scraping up any browned bits from the bottom of the pan. Sprinkle in the flour and whisk until a smooth paste forms, about 1 minute. Add the warm chicken broth in a slow steady stream, whisking constantly. Bring the liquid to a boil, whisking, then cook until the sauce is thick enough to coat the back of a spoon, about 2 minutes more. Remove the skillet from the heat. Whisk in the sour cream, parsley and mustard. Season with salt and pepper. Scrape the sauce into the bowl with the vegetables. Add the chicken and stir gently to combine. Scrape into the prepared baking dish.
In a microwave-safe bowl, melt the remaining 2 tablespoons of butter at high power, about 30 seconds. In a small bowl, toss the crumbled crackers with the poppy seeds and melted butter until well combined. Sprinkle over the chicken mixture.
Bake at 375° for 40 minutes, until the cracker topping is browned and the chicken filling is bubbling.