Heat the olive oil in a large skillet over medium-high heat. Add the mushrooms and thyme and more olive oil if needed and saute until lightly browned and tender, 5 to 10 minutes. Add the onion and season with salt and pepper. Let cook until the onions are softened, 5 to 7 minutes. Mix in the flour and mustard and cook for about 2 minutes. Whisk in the beef stock and bring to a simmer. Cook until thickened, 3 to 4 minutes. Add the grilled chicken breasts, then cover the skillet and turn down the heat to medium-low. Let simmer for about 10 minutes.
Prepare the rice according to the package directions. Remove the rice to a large bowl and stir in 2 tablespoons parsley. Place rice on a platter, then top with the chicken and mushroom sauce. Garnish with the remaining fresh parsley.