Cook ground lamb, gingerroot, and garlic in a large skillet over medium heat until browned, stirring until meat crumbles; drain.
Combine lamb mixture, cilantro, mint, sesame seeds, cumin, and salt in a bowl; stir well, and set aside.
Cut egg roll wrappers in half lengthwise. Lightly brush edges with 1 tablespoon water. Place about 1 tablespoon lamb mixture at base of a wrapper half; fold the right bottom corner over to form a triangle. Continue folding back and forth into a triangle to end of wrapper half. Repeat procedure with remaining wrapper halves and lamb mixture.
Pour vegetable oil to depth of 2 inches in a Dutch oven; heat to 375°. Fry filled egg roll wrappers 1 to 2 minutes or until golden, turning once. Drain well.
Combine teriyaki sauce and remaining ingredients; stir well. Serve wontons with peanut sauce.