Caramelized Leek Pasta

Name: Caramelized Leek Pasta
Ingredients: 2 pounds (about 4 medium) leeks, white and light green parts only (roots trimmed); 3 tablespoons unsalted butter; Kosher salt and freshly ground black pepper; 1/4 cup dry vermouth; 1 cup heavy cream; 1 large lemon; 1 to 2 tablespoons extra-virgin olive oil; 1 large garlic clove, peeled and smashed; 1 cup panko; 16 ounces lumache, conchiglie, or your preferred pasta; 1 ounce finely grated Parmigiano-Reggiano; Fresh basil leaves, roughly torn, for serving