In a large pot, heat the oil over medium. Season the short ribs all over with salt and pepper and cook, turning often, until lightly browned, 6 to 8 minutes. Transfer to a bowl; cover tightly with plastic wrap.
Add the bacon to the pot. Cook over medium, stirring occasionally, until browned, 3 minutes. Stir in the onion, carrot and garlic; season. Cook, stirring occasionally, until the vegetables soften, 5 minutes. Add the wine and cook, stirring occasionally, until the liquid is almost evaporated, about 4 minutes. Stir in the stock and tomatoes and bring to a boil.
Nestle the browned ribs into the sauce, then cover and cook over medium-low, stirring occasionally, until the meat is fork-tender, about 2 hours. Using two forks, shred the meat in the pot. Stir in the kale until wilted; season the ragu and cover to keep warm.
In a medium saucepan, boil water and cook the gnocchi according to package instructions; drain and season. Stir the gnocchi into the ragu. Divide among bowls and top with the pecorino.