For the meat sauce: In a large Dutch oven over medium-high heat, warm the olive oil. Add the ground beef and sear without disturbing until brown, 3 to 4 minutes. Break it up into smaller pieces with a wooden spoon. Season with salt and pepper and cook until deeply browned, 8 to 10 minutes. Stir in the onion and cook until softened, about 3 minutes. Add the Aleppo and cinnamon and stir to combine. Tie the thyme sprigs together with butcher’s twine and add to the meat sauce. Deglaze with the wine, reduce by half, then stir in the crushed tomatoes and 1 cup water. Reduce to a simmer and cook until the tomatoes have begun to break down, about 30 minutes.
For the béchamel sauce: In a large saucepan over medium heat, add the butter and allow to melt. Whisk in the flour and allow to toast for 1 minute. Add the nutmeg and about a quarter of the milk and whisk as the mixture cooks and bubbles. Add another quarter of the milk and cook, whisking. Once the milk is incorporated, add the rest of the milk and whisk again. This will ensure a smooth bechamel sauce. Season with salt and pepper and continue to cook, whisking, until the mixture has thickened, 3 to 4 minutes. Remove from the heat and whisk in the kefalotyri cheese until melted. Whisk in the eggs and set aside.
For the pasta: Bring a large pot of salted water to a boil and add the pasta. Do not stir as you will disturb it. In order to have even layers, the pasta needs to be cooked undisturbed, with all the noodles facing the same way. Cook the pasta for 4 minutes less than the package instructions.
Set up your grill for indirect heat. If using a charcoal grill, build the coals on one side only. If using a gas grill, heat one side only.
To assemble: Brush a 9-by-13-inch casserole dish with olive oil and set aside. Using tongs, remove the pasta from the pot and line the pasta evenly in the bottom of the prepared casserole dish. All the noodles should be facing the same direction. Add the melted butter and kefalotyri cheese and season with black pepper. Remove the bundle of thyme from the meat sauce and pour the meat sauce on top of the pasta. Using a rubber spatula, spread into an even layer without pressing down. Pour the béchamel over the meat sauce. Place the casserole dish onto the offset heat part of the grill, close the grill and bake until the top is golden brown and puffy, 40 to 45 minutes. Remove from the grill and allow to cool for at least 30 minutes before cutting into slices and serving.
Oven method: Bake uncovered at 400 degrees F for 40 to 45 minutes.
If your local market does not carry kefalotyri cheese, Pecorino Romano makes an excellent substitute!