Big Baked Ziti

• Salt
• 1 pound ziti
• 2 tablespoons EVOO – Extra Virgin Olive Oil
• 1 pound ground lamb
• 1 medium onion, chopped
• 2 cloves garlic, finely chopped or grated
• 1 carrot, peeled and finely chopped or grated
• 2 to 3 sprigs fresh thyme, leaves removed and chopped
• 2 pinches ground cinnamon
• 1 teaspoon (about 1/3 palmful) allspice
• Ground black pepper
• 1 15-ounce can whole peeled tomatoes
• 6 tablespoons butter, divided
• 4 tablespoons flour
• 3 cups milk
• A few grates fresh nutmeg
• 1 cup grated Parmigiano Reggiano or kefalotyri cheese, divided
• 2 pitas, toasted or 1 1/2 cups pita chips
• 1/4 cup flat-leaf parsley, chopped