Bring 4 quarts of water to a boil in a dutch oven over high heat. Stir in 1 tbsp salt and the pasta and cook, stirring occasionally, until just beginning to soften, about 5 minutes. Drain and toss with 1 tbsp oil. Set aside.
Wipe the pot dry, add the remaining 3 tablespoons of oil and set over medium-low heat until shimmering. Add the cremini mushrooms, onion, porcini mushrooms, and 1 tsp salt (VARIATION: No mushrooms. Add the artichokes, onion, and 1 tsp salt and cook until artichokes are lightly browned. Proceed to next step). Cover and cook, stirring often, until the mushrooms have released their liquid, about 10 mintues. Uncover, increase the heat to medium-high, and continue to cook, stirring often, until the mushrooms are dry and browned, 5 to 10 minutes.
Stir in the garlic and thyme (VARIATION: no thyme, add lemon zest) and cook until fragrant, about 30 seconds. Stir in flour and cook, stirring constantly, until golden, about 1 minute. Slowly whisk in the broth, wine, and cream.
Add the chicken breasts (VARIATION: and add bay leaves), partially cover, and bring to a simmer. Reduce the heat to low, cover completely, and cook until the thickest part of the chicken registers 160 degrees on an instant-read thermometer, 10 to 15 minutes.
Remove the pot from the heat (VARIATION: and discard bay leaves). Remove the chicken and set aside to cool; keep the sauce covered. When the chicken is cool enough to handle, shred it into bite-sized pieces. Stir the shredded chicken and 1 cup of the cheese into the sauce with the cooked pasta until well combined (VARIATION: also stir in peas and lemon juice). Season with salt and pepper to taste. Transfer to a 13 by 9-inch baking dish and sprinkle with the remaning 1 cup cheese.
TO STORE: Wrap the dish tightly with plastic wrap and then foil and refrigerate for up to 2 days or freeze up to 1 month. (If frozen, the casserole must be thawed completely in the refrigerator, about 24 hours.).
TO SERVE IF REFRIGERATED: Adjust an oven rack to the middle position and heat the oven to 400 degrees. Unwrap the dish and cover tightly with aluminum foil that has been sprayed with vegetable spray (or use non-stick foil). Bake until the sauce is bubbling around the edges, 30 to 40 minutes. Remove the foil and continue to bake until hot throughout and browned on top, 25 to 30 minutes longer. Sprinkle with the parsley before serving.
TO SERVE RIGHT AWAY: Bake the casserole in a 400-degree oven, uncovered, until the sauce is bubbling and the top is browned, 25 to 35 minutes. Sprinkle with the parsley before serving.
BAKE HALF, FREEZE HALF: Divide between two 8 by 8-inch casserole dishes or three 9 by 3-inch loaf pans and follow storage directions (above). To serve, follow directions above, reducing cooking time by 5 to 10 minutes.