Add a splash of oil to a heavy bottomed saucepan over low heat. Sauté garlic and finely diced coriander stems until completely soft. Add the laksa paste and turn the heat up to medium and cook for 2 minutes until fragrant.
Add stock and coconut milk to the pot and carefully lower the chicken breasts into the broth. Bring the broth to a rolling simmer, then reduce the heat to a very gentle simmer for about 12 minutes to poach the chicken. Remove chicken from broth and leave to rest for 2 minutes before shredding with two forks.
Add the fish sauce and lime juice and stir through. Add the shredded chicken back to the pot, let simmer until everything is warmed through.
Cook the noodles as per packet instructions and serve into four noodle bowls. Ladle over the laksa broth and chicken. Top each bowl with mung beans, coriander leaves, chilli & half boiled egg.