Cut each chicken breast in half lengthwise to create two thin pieces. Place between plastic wrap and pound to about 1/4 inch thick using a meat mallet or rolling pin. Even thickness ensures uniform cooking.

Heat olive oil over medium-high heat in a large deep skillet. Combine flour, salt, and pepper on a flat plate. Dredge each chicken piece in the seasoned flour and shake off any excess.

Cook chicken in batches of 2 to 3 pieces to avoid overcrowding. Cook for 3 to 4 minutes per side until deep golden brown and cooked through to 165 degrees F internally. Remove and set aside. Add more olive oil between batches if needed.

Keep heat at medium and melt butter in the same skillet. Add sliced mushrooms and diced onion. Cook for 3 to 4 minutes, stirring occasionally, until mushrooms are golden and slightly caramelized and onion has softened.

Stir in the flour and minced garlic. Cook for 1 minute, scraping up any browned bits from the bottom of the pan with a spoon.

Pour in the Marsala wine and whisk to combine. Simmer for 1 minute.

Reduce heat to medium-low and whisk in the chicken broth and heavy cream. Reducing the heat before adding cream prevents the sauce from breaking.

Raise heat back to a gentle simmer and cook uncovered for 8 to 10 minutes, stirring occasionally, until the sauce has turned a rich golden color and coats the back of a spoon.

Return chicken to the skillet and nestle each piece into the sauce. Heat for 2 to 3 minutes until warmed through. Serve immediately.