Cut chicken breasts in half lengthwise. Place one chicken breast at a time in a heavy-duty freezer bag (unsealed) and pound to 1/4" thickness using a mallet or rolling pin.

Combine ½ tsp salt, black pepper, and Italian seasoning with the all-purpose flour in a shallow bowl. Lightly coat the chicken breasts, shaking off excess.

Heat 1 Tbsp vegetable oil in a large skillet over medium-high heat. Sear chicken breasts for 3-4 minutes per side until golden brown. Transfer chicken to a plate and cover with foil.

Turn heat to medium. Add 1 Tbsp vegetable oil to the skillet. Add sliced mushrooms and ½ tsp salt. Sauté for about 3 minutes until mushrooms are browned.

Add sliced white onion to the skillet and sauté for another 2-3 minutes until softened and slightly browned.

Pour in the Marsala wine and ½ cup chicken broth into the skillet, scraping up any browned bits. Simmer until the liquid reduces by about 1/3, about 4 minutes.