Squid Carbonara

Ingredients

• 2 cups plus 2 tablespoons chicken broth
• cup heavy cream
• 1 cup grated Parmesan cheese
• 2 large eggs
• 12 squid tubes
• 6 tablespoons lard
• About 4 ounces pancetta (cut crosswise into lardons, 1-inch long by 1/2-inch thick)
• 2 teaspoons olive oil
• 1/4 cup Parmesan sauce, divided
• Freshly ground black pepper
• 2 tablespoons grated Parmesan, divided
• 12 chive flowers, or finely sliced chives, for garnish