Kalua Pig with Cavatelli and Chinese Broccoli

Name: Kalua Pig with Cavatelli and Chinese Broccoli
Ingredients: 1 large sheet banana leaf, about 24-by-12 inches; 4 pounds boneless pork butt; 1 tablespoon plus 1 teaspoon liquid smoke; 1 tablespoon coarse Alaea sea salt (or any coarse sea salt); Kosher salt; 8 ounces dried cavatelli pasta; 4 tablespoons unsalted butter; 1 cup grated Parmigiano-Reggiano, plus more for finishing; 2 tablespoons olive oil; 2 large cloves garlic, minced; 8 ounces baby Chinese broccoli shoots, or regular Chinese broccoli cut into 1-inch pieces