Stir together 8 cups cold water and the cornstarch in a large bowl. Add the clams, and let sit for 10 minutes. Transfer the clams to a strainer with a slotted spoon, leaving any sand at the bottom of the bowl. Rinse the clams thoroughly under cold water.
Heat 2 tablespoons water in a straight-sided medium skillet over medium heat. When the water starts to bubble, add the clams in a single layer, and cover with a tight-fitting lid. Cook just until the shells open, 7 to 9 minutes. Remove from the heat, and transfer the clams with a slotted spoon to a rimmed baking sheet to cool. Discard any clams that did not open. Pour any clam liquid from the skillet into a paper-towel-lined fine-mesh strainer set over a bowl; set aside. Wipe out the skillet.
Add 1 1/2 tablespoons of the oil to the skillet, and return it to medium heat. Add all but 2 tablespoons of the scallions to the oil, season with a few grinds of pepper and cook, stirring occasionally, until soft, 3 to 5 minutes. Add the garlic, and cook, stirring, until soft, about 2 minutes. Add the mirin, 2 tablespoons of the reserved clam liquid and 2 tablespoons water, and cook until reduced by half, about 2 minutes. Turn off the heat; set aside.
Position an oven rack in the center of the oven, and preheat the broiler. Toss the panko with the remaining 1 1/2 tablespoons oil and a few grinds of pepper in a small bowl; set aside.
Remove the top shell from each clam by carefully twisting it off, leaving the bottom shells with the clams on the baking sheet; discard the top shells. Use your fingers to separate each clam from its muscle. Put 1/2 teaspoon of the reserved scallion-garlic mixture on top of each clam. Sprinkle each with 1 teaspoon of the panko mixture, making sure that the clams are completely covered.
Broil the clams, keeping the oven door slightly ajar and watching carefully, until the panko is light golden brown, about 2 minutes. Transfer the clams to a platter, garnish with the remaining 2 tablespoons sliced scallions and serve immediately.
Mirin is a Japanese sweet rice wine available in Asian and specialty food stores.
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