How to Make It
In a large deep skillet, melt the butter in the olive oil. Add the lamb, season with salt and cook over moderately high heat for 8 minutes, breaking up the meat. Add the mushrooms and garlic and cook, stirring occasionally, until the mushrooms are tender and any liquid is evaporated, about 8 minutes. Stir in the tomato paste, rosemary and crushed red pepper and cook for 1 minute. Remove from the heat and keep warm.
Bring a large pot of salted water to a boil. Add the fettucine and cook until al dente. Drain, reserving 1 cup of the cooking water.
Add the fettucine and the reserved cooking water to the skillet and cook over moderately high heat, stirring, until the pasta is coated in a thick sauce, about 1 minute. Transfer the pasta to bowls and serve, passing the Pecorino at the table.