Cook rice according to package directions and bring a pot of water to a boil over high heat for the asparagus.
While the rice is cooking, heat EVOO in a large skillet over medium-high heat. When the oil is hot, cook the chicken breasts until brown on each side and cooked through.
Once the water is boiling, add some salt and the asparagus, and cook until tender. Drain and reserve.
When the chicken is finished, remove it from the pan and reserve. Add the butter to the hot pan and melt. Add the mushrooms to the pan and brown, about 4-5 minutes. Add the shallots and thyme, and cook until tender, about 3-4 minutes. When all the vegetables are tender, sprinkle the flour over the mushrooms and shallots, cook about 1 minute then stir in the white wine, chicken stock, Dijon mustard and heavy cream. Cook about 2 minutes, until thickened.
Serve chicken topped with the Dijon gravy and the rice and asparagus alongside.