My Ultimate Greek Moussaka

Ingredients

• 4 medium potatoes (peeled, sliced into ¼ inch slices)
• 1 medium red onion (sliced)
• 2 tablespoons olive oil
• ¼ teaspoon salt (or to taste)
• ⅛ teaspoon pepper (or to taste)
• ½ teaspoon dried thyme
• 1 teaspoon dried oregano
• 1 large eggplant (cut into ¼ inch slices)
• 1 large zucchini (sliced into ¼ inch slices)
• 1 tablespoon olive oil
• 1 medium red onion (chopped)
• 2 cloves garlic (minced)
• 1 pound ground beef
• 1 teaspoon allspice
• ½ tablespoons Italian seasoning
• 1 tablespoon tomato paste
• 15 ounces diced tomatoes (1 can)
• 8 tablespoons unsalted butter (1 stick)
• ¾ cup all-purpose flour
• 3 cups milk
• ¼ teaspoon pepper
• ¼ teaspoon nutmeg
• 3 egg yolks
• ¾ cup Parmesan cheese (grated)