In a large cast-iron casserole, heat 2 tablespoons of the oil. Add the carrot, onion and celery and cook over high heat, stirring occasionally, until slightly softened, 5 minutes. Add the lamb, coriander, fennel, cumin, rosemary and thyme; season with salt and pepper. Cook, stirring, until the liquid evaporates, 5 minutes. Stir in the tomato paste. Add the wine and cook until evaporated, 5 minutes. Add the tomatoes and their juices, along with the stock and bring to a boil. Cover partially and cook over moderately low heat until the liquid is slightly reduced, 25 to 30 minutes.
In a large pot of boiling salted water, cook the pasta until al dente. Drain, shaking well. Add the pasta to the sauce. Add the butter and the remaining 1 tablespoon of oil and toss over low heat. Serve the pasta in bowls, topped with the ricotta and mint.