Lightly season both sides of the chicken with salt and pepper. Place about 1/2 cup of flour in a shallow bowl and coat each piece of chicken, shaking off any excess.
Heat the avocado oil in a large skillet over medium heat. Once hot, add the chicken in a single layer (work in batches if needed). Cook for about 4–5 minutes per side, until golden and cooked through. Transfer to a plate and set aside.
In the same pan, add the shallot and mushrooms. Cook, stirring occasionally, until the mushrooms are tender and have some color, about 4–5 minutes. Add in garlic and saute for a minute or so. Season lightly with salt and pepper.
Sprinkle in one tablespoon of flour and stir it into the vegetables, letting it cook for about a minute to remove any raw flour taste.
Slowly pour in the chicken stock and marsala wine, stirring/whisking and scraping up any browned bits from the bottom of the pan. Let the sauce come to a simmer and cook for a few minutes, until slightly reduced and starting to thicken.
Stir in the heavy cream and adjust seasoning with salt and pepper as needed.
Return the chicken to the skillet, spooning the sauce over the top. Let everything simmer together for a couple of minutes until warmed through and coated in that sauce.