In a 5-quart Dutch oven set over medium-low heat, cook bacon, stirring occasionally, until fat has rendered and bacon is crispy, about 8 minutes. Using a slotted spoon, transfer bacon to a small bowl. Increase heat to medium-high.

Lightly season chicken all over with salt and pepper, then place it skin-side-down in the Dutch oven. Cook until well browned, 5 to 7 minutes per side. Using tongs, remove the chicken to a plate. Pour all but 2 tablespoons of fat from Dutch oven; discard excess fat.

Add mushrooms, onion, carrots, and celery to Dutch oven and cook over medium-high heat, stirring occasionally, until vegetables are tender and onion and celery are translucent, about 7 minutes. Using a wooden spoon, scrape fond from bottom and sides of pot. Return bacon and chicken to the pan; nestle chicken skin-side-up among the vegetables. Add wine and 1 cup low-sodium chicken broth or water, and season generously. (Liquid should reach about ⅔ of the way up sides of the chicken; add more water as needed.)

Bring to a simmer, then reduce heat to low. Cover pot and gently simmer until the vegetables are soft and the meat is tender, 45 to 55 minutes. Using tongs, remove chicken to a plate; set aside.

Bring braising liquid to a boil over medium-high and cook, stirring frequently, until slightly reduced, about 5 minutes.

In a small bowl, whisk cornstarch and 3 tablespoons cold water to combine. Pour cornstarch slurry into braising liquid; stir well to combine and cook until sauce is thick enough to coat back of a spoon, about 3 minutes. Remove from heat and stir in cream until well-combined. To serve, place individual thighs onto plates and ladle the vegetables and sauce over the top. Serve with crusty bread, egg noodles, or cooked farro.