East Hampton Clam Chowder

Name: East Hampton Clam Chowder
Ingredients: 12 tablespoons (1 1/2 sticks) unsalted butter, divided; 2 cups chopped yellow onions (2 onions); 2 cups medium-diced celery (4 stalks); 2 cups medium-diced carrots (6 carrots); 4 cups peeled medium-diced boiling potatoes (8 potatoes); 1 1/2 teaspoons minced fresh thyme leaves (1/2 teaspoon dried); 1 teaspoon kosher salt; 1/2 teaspoon freshly ground black pepper; 1 quart (4 cups) clam juice; 1/2 cup all-purpose flour; 2 cups milk; 3 cups chopped fresh chowder clams (1 1/2 pounds shucked clams)