Cook the Pasta:
Preheat the oven to 350°F (175°C). Cook the pasta according to the package instructions until al dente. Drain and set aside. Grease a large baking dish (about 9×13 inches) with olive oil.

Make the “Meat” Sauce:
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and garlic and sauté until softened, about 5 minutes. Add the grated carrot and cook for another 2-3 minutes.

Add the Lentils:
Add the lentils (or vegan ground meat) to the pan and stir well. Cook for 5 minutes, breaking up any large clumps if using vegan ground meat.

Add the Tomatoes and Spices:
Stir in the crushed tomatoes, tomato paste, red wine (if using), oregano, cinnamon, allspice, salt, and pepper. Bring to a simmer and cook for about 15-20 minutes, or until the sauce thickens. Stir occasionally. Adjust the seasoning as needed. If you like, stir in fresh parsley for added flavor.

Make the Vegan Béchamel Sauce:
In a medium saucepan, melt the vegan butter over medium heat. Once melted, whisk in the flour and cook for about 1-2 minutes to form a roux. Gradually add the plant-based milk while continuously whisking to avoid lumps. Keep whisking until the sauce thickens, about 5-7 minutes.

Season the Béchamel:
Once thickened, add the nutmeg, salt, pepper, and nutritional yeast (if using). Stir well and remove from heat.

Assemble the Pastitsio:
In the greased baking dish, spread half of the cooked pasta in an even layer. Top with the lentil “meat” sauce and spread evenly. Then, pour the remaining pasta on top of the meat sauce. Finally, pour the béchamel sauce over the entire casserole, spreading it out evenly with a spatula.

Bake:
Bake in the preheated oven for 30-35 minutes, or until the top is golden and bubbling. If you want a crispier top, you can broil it for an additional 2-3 minutes at the end.

Cool and Serve:
Let the pastitsio cool for 10-15 minutes before slicing and serving. Garnish with fresh parsley or more nutritional yeast, if desired.