In a large skillet, heat the EVOO, 1 turn of the pan, over medium-high heat. Add the lamb (or beef) and cook, crumbling the meat, until well browned, about 5 minutes. Season with salt, pepper and the cinnamon. Add the onion, garlic, chile and oregano (or marjoram) and cook, stirring, for 3 to 4 minutes. Stir in the tomato paste for a minute. Stir in the stock and simmer over low heat until thickened slightly, about 15 minutes.
In a saucepan, melt the butter over medium heat. Whisk in the flour and cook, stirring, for 2 minutes. Whisk in the milk and cook until thickened slightly; season with salt, pepper and nutmeg. Remove the sauce from the heat and whisk in the cheese.
To serve, spoon the meat mixture onto the rolls. Top with the sauce.