Preheat the oven to 325 degrees . Rub the short ribs with the cumin and season with salt and pepper. In a large dutch oven, heat 2 tablespoons olive oil over medium-high heat. Working in batches, add the short ribs and brown on all sides; transfer to a platter. Discard all but about 1 tablespoon of the fat from the pot.
Lower the heat to medium, add the leeks and cook, stirring, until softened, about 7 minutes. Add the garlic and tomato paste and cook for 3 minutes. Add 2 cups water, the beer and thyme. Return the ribs to the pot, cover and cook in the oven, rotating every 30 minutes, until the meat is very tender, about 3 hours.
Meanwhile, in a large pot of boiling, salted water, cook the carrots and green beans until crisp-tender, about 1 minute. Drain.
In a large skillet, heat the remaining 1 tablespoon olive oil over medium heat. Add the vegetables and cook, tossing, until warmed through; season with salt and pepper. Serve with the short ribs.
