Mix salt, baking soda, and 1 tablespoon water in bowl. Add beef and toss until thoroughly combined. Set aside.

Heat oil in medium saucepan over medium heat until shimmering. Add onion and cook, stirring frequently, until softened, about 3 minutes. Stir in garlic, cinnamon, oregano, mint, paprika, pepper flakes, and pepper and cook until fragrant, 1 to 2 minutes. Add wine and cook, stirring occasionally, until mixture is thickened, 2 to 3 minutes. Add tomato paste, beef mixture, and remaining ½ cup water and cook, breaking up meat into pieces no larger than ¼ inch with wooden spoon, until beef has just lost its pink color, 3 to 5 minutes. Bring to simmer; cover, reduce heat to low, and simmer for 30 minutes, stirring occasionally. Off heat, season with salt to taste. (Meat sauce can be refrigerated in airtight container for up to 3 days. Heat through before proceeding with step three.)

Adjust oven rack to middle position and heat oven to 375 degrees. Spray 8-inch square baking dish with vegetable oil spray and place on rimmed baking sheet. Melt butter in large saucepan over medium heat. Add flour, garlic, salt, nutmeg, and pepper and cook, stirring constantly, until golden and fragrant, about 1 minute. Slowly whisk in milk and bring to boil. Add pasta and return to simmer, stirring frequently to prevent sticking. When mixture reaches simmer, cover and let stand off heat, stirring occasionally, for 15 minutes (pasta will not be fully cooked).

Using spider skimmer, transfer pasta to prepared dish, leaving excess béchamel in saucepan. Sprinkle ⅓ cup kasseri over pasta and stir to combine. Using spatula, gently press pasta into even layer. Add ⅓ cup kasseri to béchamel and whisk to combine. Whisk egg into béchamel. Spread meat sauce over pasta and, using spatula, spread into even layer. Top with béchamel. Sprinkle remaining ⅓ cup kasseri over béchamel. Bake until top of pastitsio is puffed and spotty brown, 40 to 50 minutes. Let cool for 20 minutes. Serve.