Heat the oil in a large pot over medium heat. Cook and stir the ginger, lemongrass, and curry paste in the heated oil for 1 minute. Slowly pour the chicken broth over the mixture, stirring continually. Stir in the fish sauce and brown sugar; simmer for 15 minutes. Stir in the coconut milk and mushrooms; cook and stir until the mushrooms are soft, about 5 minutes. Add the shrimp; cook until no longer translucent about 5 minutes. Stir in the lime juice; season with salt; garnish with cilantro.