Season the chicken with salt and pepper on all sides. Melt the butter over medium heat in a large heavy-bottomed sauce pan. Add in the chicken, skin side down, and cook 5 to 6 minutes, or until the skin is golden and crispy. Turn over and cook an additional 2 to 3 minutes. Remove the chicken and set aside.

Add the remaining butter and carrots. Cook 6 minutes, stirring frequently. Add the mushrooms and lightly sprinkle with salt. Cook an additional 2 to 3 minutes, or until the mushrooms have turned golden and shed some of their moisture. Add the garlic and cook until fragrant ~ about 30 seconds.

Sprinkle the flour over the top and stir to fully saturate it with the butter. Slowly add in the chicken stock, stirring constantly, until fully incorporated with the flour. Add in the wine, heavy cream, and Dijon mustard. Bring to a simmer and season to taste with salt and pepper.

Once the sauce has thickened slightly, add in the thyme, parsley, pearl onions, and chicken (I like to tie the thyme and parsley together with kitchen twine for easier disposal). Cover the pan with a lid and reduce the heat to low. Cook until the chicken reaches an internal temperature of 165°F ~ about 30 to 40 minutes. Remove the lid and squeeze the lemon juice over the top. Discard the thyme and parsley. Garnish with chopped parsley, if desired.

Serve immediately! Best served over mashed potatoes. Enjoy!