Rub the chicken thighs with the salt and refrigerate for at least 1 hour or overnight.
Empty the flour into a shallow dish. Season the chicken with the pepper and then dredge the chicken in the flour until lightly coated. Set aside.
Heat the butter in a large pot over medium-high heat. Cook the chicken until browned on both sides, about 5 minutes per side. Place browned chicken on a plate or platter and cover loosely with aluminum foil to keep warm. Set aside.
Reduce the heat to medium-low and add the mushrooms and garlic, stirring to coat in the butter. Cook until the mushrooms have released their water, shrunk, and darkened in color, about 15 minutes, stirring every 3 minutes or so.
Add the wine, broth, soy sauce, thyme leaves, and the browned chicken and raise the heat to medium, bringing the mixture to a boil. Ladle the pan juices over the chicken. Place the pid partially covering the pot, keeping it a bit open for the steam to escape.
Once the chicken is cooked all the way through (a thermometer inserted towards the bone reads 165 degrees Fahrenheit and the juices of the chicken run clear), taste the mushrooms and add additional salt and pepper as desired. Garnish with fresh parsley and serve.