In a small bowl, mix 1 Tbs. of the ginger, the soy sauce, vinegar, 2 Tbs. water, and about a quarter of the scallions. Set the dipping sauce aside.
Rinse the cod and pat dry it with paper towels. Season both sides lightly with salt and pepper. Put the flour in a shallow bowl. Put the egg whites in a medium bowl and whisk until a thick foam forms on the surface. To the egg whites, add the garlic, chiles, and the remaining ginger and scallions and mix well.
Heat the oil in a large nonstick skillet over medium heat. Dredge each piece of cod on both sides first in the flour and then in the egg whites, using your hands to press the scallions and chiles onto the fish. Transfer to a plate.
When the oil is hot (it will bubble if you put a scallion ring in it), add the cod, spacing the pieces evenly (you may have to cook them in two batches), and raise the heat to medium high. Turn the fish over after 3 minutes. Reduce the heat to medium and cook until the fish is firm to the touch and flakes apart easily when pierced with a fork, about another 4 minutes. Serve immediately with the dipping sauce and the lime wedges on the side.
Serve with white rice and spinach sautéed with garlic, or with soba noodles in broth.