Preheat oven to 400 °F.
In a large oven-safe Dutch oven, or stockpot, heat oil until it starts to sizzle. Add mushrooms and cook for about 2 minutes (just until they start to brown).
Reduce heat to medium-high, add onions, salt, and pepper and saute until the liquid is nearly evaporated.
Add garlic and cook for 1-2 more minutes (take care not to burn)
Add Marsala, stirring occasionally, until it has been reduced by half (or more).
Add butter, and once melted, add flour and stir until it has fully incorporated.
Add chicken broth, a little at a time, scraping the bottom of the pan and stirring constantly, repeat until all broth has been added.
Simmer for 2 minutes, stirring frequently; until the sauce begins to thicken.
Remove pan from heat.
Add noodles, chicken, mozzarella, parsley, and half the parmesan and stir to combine.
Top with remaining parmesan.
Bake for 25 to 30 minutes, until edges of pasta, are golden brown.