Pat chicken dry and season generously with salt and pepper.
In a large deep pan or Dutch oven, melt the butter over medium heat. Add chicken pieces skin side down and cook, turning occasionally, until all sides have browned, approximately 10-12 minutes. Chicken will not be cooked through. Transfer chicken to a plate and set aside.
Add shallot and garlic to the same pan and cook until shallots begin to soften, 3-4 minutes. Add sausage and continue cooking until sausage begins to brown and shallots are translucent.
Sprinkle flour in a skillet.
Add wine and cook for 3-4 minutes, scraping up any browned bits. When the wine mixture has reduced slightly, stir in chicken broth.
Return the chicken to the pan nestling it down into the broth.
Add heavy cream to the pan and season with salt and pepper to taste. Continue to simmer at medium heat until chicken is cooked through, approximately 45 minutes.
While the chicken is cooking, trim the brussels sprouts and cut in half.
Heat a dry skillet over medium heat and cook brussels sprouts until they get nicely browned but not charred.
Ten minutes before the chicken is finished cooking, add the brussels sprouts to the chicken. Add lemon juice and continue cooking for 10 minutes until chicken is cooked through.
See recipe tip for serving suggestions. Garnish with lemon slices, if desired. Enjoy!