Make the dipping sauce: Combine all the ingredients in a bowl. Let it sit for the flavors to develop while the fish cooks.
Preheat the grill. Squeeze the lime juice into a large bowl and throw in the halves. Add the soy sauce, chiles, ginger, cilantro, and mint; season with salt and pepper and give it a good stir. Place the salmon in the center of the banana leaf and stuff it with the lime juice mixture. Fold the banana leaf over the fish to completely encase it and tie closed with kitchen string. Place onto a medium-hot grill. Cook until the fish is cooked through, about 35 to 40 minutes. Serve with the dipping sauce.