In a food processor, blend 1/3 of the shrimp into a paste. Add remaining shrimp; pulse until finely chopped. Transfer to a bowl. Add garlic, ginger, jalapeno, 1/4 cup cilantro, 2 green onions, 1/4 cup peanut sauce, bread crumbs and salt; combine with a fork. Divide into 4 portions. Pat with fingertips to flatten to about 4 inches wide. Refrigerate.

Whisk remaining peanut sauce with lime juice and oil. Mix slaw with remaining onion and cilantro; toss with dressing. Refrigerate.

For charcoal grill: Build a hot fire on one side of grill. Replace rack. When coals are covered with white ash, add burgers. Cover and cook, turning only once, until opaque throughout, about 3 1/2 to 4 minutes per side.

Grill pitas until spotty brown and warm, a minute or so per side. Split crosswise. Place a burger on each of 4 pita halves. Top with slaw, then remaining pita halves.