With the back of a knife or in mortar and pestle, smash all of the aromatics (lime leaves, galangal root, lemongrass) until fragrant.
In a medium hot pan, simmer curry paste and aromatics with half of the coconut milk until fragrant, about 1 minute. Add remaining coconut milk, fish sauce, and brown sugar. Stir to combine.
Add carrot medallions, onion, potato cubes, eggplant, and red pepper with chicken broth. Simmer for 30–45 minutes or until vegetables are tender.
Add shredded chicken and frozen peas. Bring back to a simmer and simmer for 2 minutes or until chicken is warm. Add lime juice, mix and serve over rice noodles.
For the rice noodles, cook according to package instructions and add to soup when serving.