Preheat the oven to 450 degrees F.
Spread one tablespoon of butter in a 13 by 9 by 2-inch baking dish. Melt one tablespoon each of butter and oil in a deep large cast iron skillet. Heat to medium-high. Season the chicken with ¼ teaspoon each of salt and pepper add the chicken to the cast iron skillet and cook until pale golden and just cooked to 165 degrees, about 4 minutes per side. Transfer the chicken to a plate to cool slightly, then shred the chicken into bite-size pieces. and add chicken to a bowl. Add one tablespoon of butter and oil to the same pan. Add the mushrooms and saute over medium-high heat until the liquid from the mushrooms evaporates and the mushrooms become lightly browned. Add the onion, garlic, and thyme, and saute until the onion is translucent, about 8 minutes. Add the wine and simmer for about 2 minutes. Transfer the mushroom mixture to the bowl with the chicken.
Melt one tablespoon of butter in the same pan over medium-low heat. Add the flour and whisk for two minutes to create a roux, then whisk in the milk, cream, broth, nutmeg, one teaspoon salt, and 3/4 teaspoon pepper. Increase the heat to high. Cover and bring to a boil, then uncover, and simmer until the sauce thickens, whisking often, about 10 minutes.
While the cream sauce is simmering bring a large pot of salted water to a boil. Add the linguine (or pasta of choice) and cook until it is al dente. Drain and add the linguine, sauce, artichoke hearts, and parsley to the chicken mixture. Toss until the sauce coats the pasta and the mixture is well blended.
Transfer the pasta mixture to the prepared baking dish. Stir the cheese and bread crumbs in a small bowl to blend. Sprinkle the cheese mixture over the pasta. Drizzle with the remaining 1 ½ tablespoons of butter. Bake, uncovered, until golden brown on top and the sauce bubbles, about 25 minutes.