In a medium saucepan, warm the peanuts over moderate heat, about 1 minute. Add the sake, soy sauce, and mirin and cook over low heat, stirring, until the liquid is reduced and coats the peanuts, about 5 minutes. Spread the peanuts on a parchment paper-lined plate and let cool.

In a blender, add the lime juice, fish sauce, chile sauce, water, garlic, and Thai chile and puree the dressing until smooth.

Bring a large pot of water to a boil and fill a bowl with ice water. Add the bean sprouts to the boiling water and blanch for 10 seconds. Using a slotted spoon, transfer the bean sprouts to the ice water to cool, then drain and pat dry. Fill the bowl with more ice water. Add the rice vermicelli to the pot and cook until tender, about 5 minutes. Drain the noodles and transfer them to the ice water to cool. Drain again, shaking off the excess water; pat dry with paper towels. Wipe out the bowl. Cut the noodles into 4-inch lengths and return them to the bowl. Add the bean sprouts, cucumber, mint, and scallions.

Put the shrimp in a large, resealable plastic bag. Add the flour, seal and shake to coat. Tap the excess flour off the shrimp. Put the eggs and panko in 2 separate bowls and line a baking sheet with wax paper. Working in batches, dip the shrimp in the egg and then in the panko, pressing the crumbs to help them adhere. Transfer the shrimp to the baking sheet.

In a large, deep skillet, heat the oil to 340 degrees. Add half of the shrimp and fry over high heat, turning once, until they are golden, about 2 minutes. Drain on paper towels and sprinkle the shrimp with salt. Repeat with the remaining shrimp.

Coarsely chop the peanuts. Add the dressing to the rice noodles and toss to coat. Transfer the noodle salad to a platter and top with the shrimp and chopped peanuts. Serve right away.

The peanuts can be stored in an airtight container for 2 days. The dressing can be refrigerated for 2 days.