Vegetarian Moussaka

Ingredients

• For the Vegetables:
• 1 ½
  pounds eggplant (2 to 3 eggplants, cut lengthwise into 1/4-inch slices)
• 1 ½
  pounds zucchini (cut lengthwise into 1/4-inch slices)
• Kosher salt, to taste
• 1 ¼
  pounds potatoes
• 4
  egg whites (reserving the yolks for béchamel)
• 2
  cups breadcrumbs
• For the Tomato Sauce:
• 2
  tablespoons olive oil
• 1
  medium onion (diced)
• 2
  garlic cloves (minced)
• 1
  (15 ounces) can chickpeas (drained, rinsed, and mashed)
• 1
  (15 ounces) can diced tomatoes (with liquid)
• 2
  tablespoons tomato paste
• ¼
  teaspoon cinnamon (ground)
• 1
  teaspoon oregano (dried)
• ½
  teaspoon cumin (ground)
• 1
  teaspoon sugar
• Salt and pepper, to taste
• For the Béchamel Sauce:
• ½
  cup unsalted butter (1 stick)
• ½
  cup all-purpose flour
• 3
  cups milk (warmed)
• 4
  egg yolks (beaten)
• A pinch of ground nutmeg
• For Assembly:
• 3
  tablespoons breadcrumbs
• ¾
  cup grated Kefalotyri (or Parmesan cheese)