In a blender or food processor, pulse shrimp, ginger, and garlic together into a paste. Place in a medium bowl. Fold in soy sauce, cornstarch, scallions, cilantro, and water chestnuts.

Heat oven to 350 degrees. Cut phyllo sheets into 4-inch squares. Brush one square lightly with oil. Place a second square on top. (Keep the rest of the phyllo covered with a lightly dampened cloth until ready to use.) Spoon about 2 teaspoons of shrimp mixture into center. Gently pull edges of phyllo to center and twist to seal. Brush each “moneybag” with oil. Place on a parchment- or Silpat-lined baking sheet. Repeat with remaining filling and dough.

Bake 15 to 20 minutes. When cool enough to handle, tie a chive bow around each piece. Serve hot, with dipping sauce.