Season the chicken with the salt and pepper. In a large pan over medium heat, warm the oil. Add the chicken and cook for about 5 minutes per side, until golden brown. Remove from pan and set aside.
In the same pan, add the vermouth, thyme, and garlic, bringing to a simmer and reduce by half, cooking about 5-7 minutes. Remove pan from the heat and stir in the dijon mustard until a smooth sauce is made. Pour over the chicken and sprinkle with fresh parsley.