Heat the oven. Preheat oven to 375°F. Wrap aluminum foil around the bottom of a 7" springform pan to prevent leaks.
Cook the pasta. Heat a large pot of water over medium-high heat. When the water is boiling add the pasta and cook for 7-8 minutes until al dente. Remove from stovetop and drain.
Make the meat sauce. While the pasta is cooking add the olive oil to a large skillet and heat over medium-high heat. Add the ground beef and cook for 5 minutes until it begins to crumble. Add the onions, garlic, cinnamon, nutmeg and cardamom. Continue cooking until the beef is cooked through. Add the wine and the tomatoes. Stir to incorporate. Remove from heat and set aside until you are ready to assemble the pie.
Make the cheese sauce. Add the milk, egg, pepper, salt and nutmeg to a medium saucepan. Whisk to combine. Heat over medium heat, stirring constantly, until small bubble form at the edge of the pan. Remove from heat and stir in the feta until it is mostly melted. You will still see small chunks of feta in the cheese sauce.
Assemble the pie. Add the spaghetti to the meat sauce. Using a pair of kitchen tongs, stir to incorporate the two. Add the spaghetti mixture to the springform pan. Pour the cheese sauce over the mixture in the pan.
Bake the spaghetti. Place the springform pan on a baking sheet and bake for 25 minutes. Sprinkle with grated parmesan and bake for an additional 5 minutes. Remove from oven and let cool for 5 minutes. Remove springform pan ring and serve.