Combine garlic, 1 tablespoon oil, soy sauce, red pepper flakes, and hoisin sauce in a medium bowl. Toss shrimp in mixture. Cover and refrigerate for 1 hour.
Place wrappers on work surface and cover with a damp kitchen towel. Working with 1 wrapper at a time, brush edges of wrapper with a beaten egg. Place a shrimp diagonally across the center and fold wrapper around shrimp. Place the chives in a bowl of hot water for 1 minute. Drain and tie 1 chive around each wonton-wrapped shrimp. Trim off excess chive. Cover with a damp kitchen towel and set aside. Repeat with remaining wrappers.
Heat the remaining 3 cups oil in a large wok until 375 degrees F.
Working in batches, add wrapped shrimp and fry until golden, 1 to 2 minutes. Using a slotted spoon remove from the oil and drain on paper towels. Garnish with cilantro and serve hot with Cilantro Lime Sauce.
Cilantro Lime Dipping Sauce:
4 tablespoons fish sauce
4 tablespoons rice vinegar
4 tablespoons fresh lime juice
2 teaspoons mirin
2 tablespoons Sriracha sauce
4 tablespoons finely chopped cilantro leaves
Combine fish sauce, vinegar, lime juice, mirin, and Sriracha sauce. Just before serving stir in cilantro. Divide sauce among 4 small bowls for dipping and serve with the Wonton Wrapped Shrimp.
