Place a large pot over medium heat and add a small amount of olive oil.
Add the diced yellow onion along with a generous pinch of coarse kosher salt. Cook until the onion has softened and just turned translucent.
Add the ground beef. Cook while stirring and breaking the meat apart with a wooden spoon until no pink remains.
Mix in the tomato sauce and ground cinnamon. Season with additional salt according to taste, then bring the mixture to a simmer.
Cover the pot with the lid positioned slightly ajar. Allow the sauce to stew for 3 hours, stirring it from time to time.
When cooking is complete, allow the meat sauce to cool before transferring it to the refrigerator overnight.
Before beginning the final assembly, allow the chilled meat sauce to come to room temperature or warm it gently.
Shred enough kasseri, Asiago, or Italian cheese blend to provide at least 4 cups. Set the cheese aside for layering.
Bring a large pot of generously salted water to a full boil.
Add the pastitsio noodles or mostaccioli and cook until al dente. For the proper texture, remove the pasta approximately 1–2 minutes before the cooking time specified on the package.
Drain thoroughly. Once the pasta has cooled sufficiently to handle, transfer it to a large bowl.
Beat 1 egg, pour it over the noodles, and use your hands to distribute the egg thoroughly throughout the pasta.
Preheat the oven to 350°F.
Lightly grease a lasagna pan or other large baking dish with a drizzle of olive oil or a coating of nonstick cooking spray.
Arrange all of the egg-coated pasta evenly across the bottom of the prepared baking dish.
Scatter approximately one-third of the shredded cheese evenly over the pasta.
Using a slotted spoon, distribute all or most of the prepared meat sauce over the cheese. Leave sufficient room at the top of the dish for the béchamel.
Cover the meat layer with another one-third of the shredded cheese. At this stage, the casserole should consist of pasta, cheese, meat sauce, and a second cheese layer.
Melt 8 tablespoons of unsalted butter in a large, heavy-bottomed pot over medium heat.
Add the all-purpose flour and whisk continuously for approximately 1–2 minutes, until the butter and flour are completely incorporated.
Gradually pour in 5 cups of whole milk while whisking constantly to maintain a smooth, lump-free consistency.
Continue cooking and whisking until the mixture just begins to boil and bubble. Remove the pot from the heat.
In a separate bowl, use a hand mixer to beat 3 eggs together with the additional 1/2 cup of whole milk.
Slowly add the egg-and-milk mixture to the hot sauce while whisking continuously.
Return the pot to medium-high heat. Continue whisking until the béchamel becomes thick and bubbly.
Remove it from the heat once the proper consistency has developed, then allow it to stand for several minutes.
In a small saucepan, melt the remaining 4 tablespoons of unsalted butter.
After the béchamel has rested briefly, pour it evenly over the assembled meat and cheese layers. Spread it across the entire surface.
Sprinkle the remaining one-third of the shredded cheese over the béchamel.
Drizzle or spoon the melted butter over the cheese. Less than the full amount may be used if a lighter topping is preferred.
Set the baking dish on a baking sheet and transfer it to the preheated 350°F oven.
Bake for 1 hour, or until the center is bubbling and the surface is attractively browned.
For deeper browning, switch the oven to broil and continue cooking for another 3–5 minutes, monitoring the pastitsio closely to prevent burning.
Remove the finished pastitsio from the oven and allow it to stand for 10 minutes before cutting.
This brief resting period helps the layered casserole firm sufficiently for cleaner slices while preserving its moist interior.