Place chicken in a 1-½- or 3-qt. slow cooker. In a bowl, combine the next 6 ingredients; pour over chicken. Cook, covered, on low until a thermometer inserted in chicken reads 165°, about 4 hours. Remove chicken; cool slightly. Shred chicken with 2 forks and return to slow cooker.
In a large saucepan, cook noodles according to package directions. In a small nonstick skillet, heat butter over medium heat. Pour in eggs; cook and stir until eggs are thickened and no liquid egg remains.
Drain noodles. Stir eggs and noodles into slow cooker. Top with green onions, peanuts and cilantro.
