In a jar with a tight-fitting lid, combine broth, peanut butter, and cornstarch. Shake to blend well; set aside.

In a large nonstick skillet, heat oil over medium-high heat and add ginger and garlic. Cook 30 seconds, then add beef and brown, breaking up with a spoon, until cooked through, about 5 minutes. Shake sauce again, then pour into skillet and cook for 2 to 3 minutes, until thickened. Remove from heat, stir in carrots, green onion, and soy sauce. Serve wrapped in lettuce leaves, garnished with peanuts and cilantro, if desired.