Make the stew

1. Season the chicken with 1/2 tsp. salt and 1/4 tsp. pepper. Heat the oil in a 10- to 11-inch straight-sided saute pan over medium-high heat. Cook the chicken, flipping once, until lightly browned, about 10 minutes. Transfer the chicken to a plate. Pour off all but about 2 tbsp of fat in the pan. Reduce the heat to medium, add the onion to the pan and saute until translucent. Sprinkle the flour over the onions.  Stir for 1 minute until well incorporated. Gradually whisk in the broth and bring to a simmer. Return the chicken to the pan, reduce the heat to medium low, cover, and simmer gently, turning once, until the chicken is very tender, about 15 minutes. Transfer the chicken to a clean plate and let cool briefly.
2. Meanwhile, stir the mushrooms, fennel, carrot,and thyme into the sauce. Cover and simmer until tender, 5 to 6 minutes. Stir in the mustard and keep warm.
3. When the chicken is cool enough to handle, pull the meat from the bones, shred into bite-size pieces (discard the skin and bones), and add to the sauce. Season to taste with salt and pepper and keep warm.

Make the whipped potatoes

1. Peel and quarter the potatoes. Put them in a 6-quart saucepan; add enough water to cover and 2 tsp. salt. Cover and bring to a boil over high heat. Uncover, reduce the heat as needed to keep the water from boiling over, and cook until tender when pierced with a fork, 12 to 15 minutes. Drain well.
2. With an electric mixer on medium-low speed, beat the potatoes until they are broken up, 1 to 2 minutes. Add the milk and the butter, and beat on high speed, scraping the sides and bottom of the pot occasionally, until fluffy, 1 to 2 minutes.  Season to taste with salt and pepper and keep warm.
3. Scoop a mound of potatoes in the centre of each soup plate.  Spoon the stew around the potatoes and serve immediately.