Place chicken breasts between plastic wrap and pound to an even 1/2-inch (1.25cm) thickness. Season both sides with salt and pepper. Dredge in all-purpose flour, shaking off excess.

Heat 2 tbsp olive oil and 1 tbsp butter in a large skillet over medium-high heat. Sear chicken for 4-5 minutes per side until a deep, golden-brown crust forms. Remove to a plate and cover with foil.

Lower heat to medium, add 1 tbsp butter, and toss in the sliced cremini mushrooms. Let sit undisturbed for 3 minutes, then stir and sauté for 4 more minutes until deeply browned.

Push mushrooms to the skillet edges. Add diced shallot and minced garlic to the center. Sauté for 1 minute until fragrant.

Pour in Marsala wine, scraping the browned bits off the bottom. Reduce wine by half (3-4 minutes). Whisk in chicken broth and heavy cream.

Simmer the sauce for 5 minutes. Meanwhile, boil the egg noodles in salted water until tender, then drain. Return chicken to the sauce for 2-3 minutes. Turn off heat and swirl in the remaining 1 tbsp butter.

Serve the golden-brown chicken on a bed of wide egg noodles in a shallow white bowl. Spoon the glossy, light-brown sauce and mushrooms over the top. Garnish with chopped fresh parsley.