Coarsely chop shrimp in processor. Add egg, green onion, lime juice, mustard, cilantro, hot pepper sauce, salt, and pepper. Blend in using on/off turns. Add 1 cup panko and blend in using on/off turns. Form the mixture into twelve 3-inch-diameter cakes. Roll cakes in remaining 1 cup panko; transfer to waxed-paper-lined baking sheet. Refrigerate for 10 minutes. (Can be made up to 4 hours ahead. Cover and refrigerate.)
Heat 2 tablespoons peanut oil in heavy large skillet over medium-high heat. Working in batches, fry cakes until cooked through and golden brown on both sides, adding more oil to skillet as needed, about 6 minutes.
In a medium bowl, add the mayonnaise, white wine, and lime juice and mix thoroughly. Next, add the fresh ginger, chili garlic sauce, and sesame oil and finish mixing.
Spoon 2 tablespoons of Spicy Aioli onto each of 6 plates. Place two shrimp cakes on each and serve immediately.