How to Make It
Preheat the oven to 350°. In a medium skillet, cook the bacon over high heat, stirring, until crisp, about 6 minutes. Add the mushroom stems and shallot, season with salt and pepper and cook, stirring, until the stems are tender and lightly browned, about 8 minutes. Add the thyme and goat cheese and let cool slightly.
Arrange the chicken thighs on a work surface, skin side down. Using a meat pounder, lightly pound the thighs until they are a scant 1/2 inch thick. Spread the mushroom mixture evenly over the thighs and roll them up; the skin should almost wrap around the meat. Tie each bundle with kitchen string in 2 places.
In a large, ovenproof skillet, heat the olive oil. Season the chicken with salt and pepper and add the bundles to the skillet. Cook over moderately high heat, turning, until lightly browned all over, about 5 minutes. Turn the chicken skin side up. Transfer to the oven and roast for about 12 minutes, until the chicken is cooked through. Light the broiler and broil 6 inches from the heat for about 1 minute, until the skin is browned and crispy. Transfer the chicken to a plate and cover loosely with foil.
Pour the chicken fat and pan drippings into a bowl and skim off the fat, reserving 1 teaspoon in the skillet. Whisk in the flour and cook over moderate heat until foamy. Whisk in the chicken broth and cook, scraping up any bits stuck to the pan with a wooden spoon, until slightly thickened, about 3 minutes. Pour the reserved pan drippings and any accumulated juices from the chicken into the sauce and season with salt and pepper. Remove the strings from the chicken thighs, drizzle with the gravy and serve.