Coarsely chop shrimp into 1/2-inch pieces. Set aside. Reserve a few tablespoons of sliced scallion greens for serving.
Combine garlic, jalapeño, remaining scallions, cilantro, lime zest, and a large pinch of salt in the bowl of a food processor. Pulse until everything is finely minced. Add half of the shrimp, the mayo, the cornstarch, and the egg white. Pulse until the mixture forms a coarse paste, about 5 or 6 pulses. Add the remaining shrimp and pulse two or three times to combine everything. Some of the shrimp will be chunkier.
Transfer the mixture to a bowl and add 1/4 cup of the panko breadcrumbs. Fold in with a spatula or your hands. The mixture should be soft and should just hold its shape if you form a ball. If it’s too soft, add more breadcrumbs a little at a time until a ball just holds together. It will stiffen up more when it gets cold. Chill mixture for at least 30 minutes and up to a day.
Once chilled, use wet hands and a tablespoon (or portioning scoop) to form the mixture into bite-sized patties. Transfer to a large plate as you go. When all the patties are formed, heat a few tablespoons of oil in a large skillet over medium high heat until shimmering. Fry patties in batches until golden brown and cooked through, turning once, 3 to 4 minutes total.
To make the dipping sauce, mix sweet chili sauce, fish sauce and lime juice together.
Serve warm, scattered with cilantro and finely sliced scallions along with dipping sauce.