How to Make It
Preheat the oven to 325°. In a large, deep, ovenproof skillet, heat the olive oil. Add the soppressata slices in a single layer and cook over high heat, turning once, until they are crispy, about 3 minutes. Transfer the soppressata to a paper towellined plate and let cool.
Season the chicken thighs with salt and pepper and add them to the skillet. Cook over moderately high heat, turning once, until browned, about 8 minutes. Transfer the chicken to a plate.
Add the onion, carrot and garlic to the skillet and cook over moderately low heat, stirring, until softened, about 8 minutes. Add the wine and cook until nearly evaporated, scraping up any browned bits stuck to the pan, about 5 minutes. Add the stock and bring to a boil. Nestle the chicken and thyme into the broth and cover tightly. Transfer to the oven and cook for about 1 hour, until the chicken is very tender.
Transfer the chicken thighs to a plate and pull the meat from the bones. Discard the skin and spoon off as much fat as possible from the broth in the skillet.
Add the greens to the skillet, cover and cook over moderate heat until they are wilted, about 5 minutes. Return the chicken thighs to the skillet and stir in the butter. Cover and keep warm.
Bring a large pot of salted water to a boil. Add the gnocchi and cook according to the package directions. Using a slotted spoon, transfer the gnocchi to the ragout and gently stir to combine. Spoon the ragout into wide bowls. Crumble the crisp soppressata on top and serve, passing the pecorino at the table.