How to Make It
Preheat the oven to 400°. On a large rimmed baking sheet, place the squash cut side up and rub the flesh all over with the olive oil. Sprinkle generously with salt and pepper and roast for about 1 hour, until the squash is easily pierced with a knife. Let cool slightly and scoop out the flesh onto the baking sheet.
Meanwhile, in a medium enameled cast-iron casserole, melt the butter over moderate heat until the foam subsides. Add the onion and cook, stirring occasionally, until it begins to soften, about 3 minutes. Add the mushrooms and cook, stirring occasionally, until softened and the mushroom liquid has evaporated, about 5 minutes. Add the paprika and cook, stirring, for 1 minute, then add the flour and cook, stirring constantly, for 1 minute. Add the broth in a steady stream, whisking until the sauce thickens, about 3 minutes. Add the chicken and cook, covered, over moderately low heat until the chicken is just cooked through, 10 to 15 minutes. Add the squash and parsley and let stand until heated through, about 1 minute. Serve hot.