Pat the chicken breasts dry with a paper towel.
Cut each breast in half horizontally into two thinner cutlets. Alternately, place the chicken under a layer of plastic wrap and pound to an even thickness.
Season the chicken breast with salt and pepper.
Add 1 Tbsp olive oil to a large skillet.
Heat over medium until the oil starts to sizzle.
Add the chicken breasts to the hot pan and cook until browned, about 5 minutes.
Flip and cook for an additional 3-5 minutes.
Remove the cooked chicken to a tray and cover to keep warm.
Repeat with any remaining cutlets.
Add wine to the pan to deglaze and scrape the brown bits from the bottom.
Add garlic and onion and cook until fragrant.
Add butter, 1/2 cup broth, and mushrooms to the skillet and cook on medium until the mushrooms are well done, about 10 minutes.
Add the remaining ingredients to the pan and simmer for 5 minutes.
Add chicken and plate juices back to the pan and spoon the sauce over the chicken.
Simmer in the sauce until the chicken is heated through and the sauce has reduced slightly.
Serve over rice or noodles.