Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1 ladle full of pasta cooking water.
While the pasta is working, in a large skillet, heat the EVOO, 2 turns of the pan, over medium-high heat. Add the lamb and cook, crumbling it, until browned, about 5 minutes. Add the tomatoes and cook, tossing, until they burst, 3 to 4 minutes. Add the shallot and garlic, season with salt and pepper and cook until softened, 3 to 4 minutes.
Stir the reserved pasta cooking water into the lamb ragu. Add the pasta, mint and parsley and toss. Top the pasta with the cheese.