East Hampton Clam Chowder

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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)