Cook Penne pasta to al dente stage according to package directions. Drain, reserving ½ cup of pasta liquid. Set aside.
Heat 2 tablespoons of unsalted butter in a large Dutch oven over medium heat. Add chicken, salt, and pepper. Cook stirring until chicken is no longer pink, about 3 to 4 minutes. Remove chicken from Dutch oven.
Add onions to Dutch oven; cook, stirring occasionally, until tender and lightly browned, about 7 minutes.
Add garlic; cook until fragrant, about 30 seconds.
Increase heat to medium-high; add mushrooms. Cook, stirring frequently, until all liquid has evaporated, about 2 minutes.
Add Marsala; cook, scraping up bottom bits until reduced by half, 2 to 3 minutes.
Reduce heat to medium; return cooked chicken to Dutch oven. Add chicken broth and cream. Stir to combine.
Add cooked pasta and the remaining 1 tablespoon of butter. Stir to combine. Cook until bubbly.
Reserve 2 tablespoons of Parmesan cheese. Add Mozzarella cheese and remaining Parmesan cheese; cook, stirring, until the cheese is melted. If necessary, add some or all of the reserved pasta liquid. Correct the seasonings.
To serve, sprinkle on reserved 2 tablespoons of Parmesan cheese. If desired, garnish with minced parsley or chives.
Yield: 6 servings.