Place all ingredients except cilantro in a food processor or blender and blend until smooth. Stir in finely chopped cilantro leaves. Let stand for 30 minutes to allow flavours to blend.
Chop the raw shrimp into very fine pieces. If using a food processor, pulse to chop, watching carefully to prevent over processing. The shrimp should be finely chopped, not turned into paste. Transfer to a medium bowl.
Whisk two egg whites until frothy (or whip them in the now-empty food processor --no need to wash it out.) Add to the bowl of shrimp along with minced garlic, ginger, fish sauce, chilies, cilantro, cornstarch and 1/2 cup Panko crumbs.
Gently combine without overmixing. Form into patties. You can make small 1-inch diameter patties for appetizers, or larger ones for a main course. Coat completely with Panko crumbs and place on a baking sheet.
At this point you can cover and refrigerate for up to 1 day until you're ready to fry them.
Heat a skillet (preferably cast iron) over medium-high heat. Add oil and heat until it shimmers. Carefully add the shrimp cakes. Fry on one side until lightly browned 3-4 minutes for the small size, longer for the larger size, then turn and fry on the other side for 3-4 minutes. Remove to paper towel, then transfer to a serving plate and serve with Mango Dipping Sauce.
Gluten-free Panko crumbs are available in supermarkets and work very well in this recipe.