- Adjust an oven rack to the middle position and heat the oven to 475 degrees. Cook the lamb in a 12-inch ovensafe nonstick skillet over medium-high heat, breaking apart the meat, until no longer pink and the fat has rendered, 3 to 5 minutes. Transfer the lamb to a strainer set over a medium bowl and let drain, reserving 1 tablespoon of the fat.
- Add the reserved tablespoon fat to the skillet and return to medium heat until shimmering. Add the onion, cinnamon, and nutmeg and cook, stirring often, until softened, 5 to 7 minutes. Stir in the garlic, tomato paste, and oregano and cook until fragrant, about 30 seconds.
- Stir in the broth, 1/2 cup of the cream, and 1/2 teaspoon salt, then add the pasta and drained lamb. Increase the heat to high and cook at a vigorous simmer, stirring often, until the pasta is tender, 9 to 12 minutes.
- Whisk the remaining 1/2 cup cream and cornstarch together in a small bowl, then stir into the skillet and continue to simmer until slightly thickened, about 1 minute. Off the heat, stir in 1/2 cup of the Pecorino and season with salt and pepper to taste. Sprinkle the remaining 1/2 cup Pecorino over the top and bake until lightly browned, 5 to 10 minutes. Serve.