Step 1
Bring a large pot of water to a boil for the noodles.
Step 2
In a large skillet, melt the butter over medium-high heat. When it foams, add the mushrooms and cook, stirring often, until browned, 10 to 12 minutes.
Step 3
Meanwhile, shred or chop the chicken meat. (Reserve the skin and bones for stock.)
Step 4
Add the shallots, carrot, celery, thyme, rosemary, garlic, and bay leaf to the mushrooms; season with salt and pepper. Cook, stirring often, until the celery and shallots soften, 3 to 5 minutes. Sprinkle with the flour. Cook, stirring constantly, until the flour is mixed in, about a minute. Add the Marsala and stir until absorbed, about 3 minutes. Stir in the stock. Reduce heat to low. Stir in the cream. Mix in the chicken. Let the sauce simmer while you cook the noodles.
Step 5
Salt the boiling water and add the noodles. Cook until 1 minute shy of the package directions. Scoop out about 1/2 cup of the cooking water. Drain the noodles.
Step 6
Toss the egg noodles and half the herbs with the sauce. Add some of the reserved cooking water if the noodles are too dry. Divide among bowls or serve in a large bowl. Top with the remaining herbs.