In a Dutch oven, heat vegetable oil over medium heat. Combine ginger, lemongrass and curry paste in a small bowl, mixing until well blended. Cook the curry paste mixture in oil for a minute or two until the paste mostly dries out.
Slowly add in the chicken broth, stirring to fully incorporate the curry paste mixture. Add fish sauce and palm sugar. Simmer for 15 minutes.
Stir in the coconut milk and mushrooms. Simmer over medium low heat for about 5 minutes or until the mushrooms are soft. Add the shrimp and continue simmering until they are cooked through, approximately 5 minutes.
Remove from heat and add the lime juice. Taste and season with additional salt, if needed. Ladle into bowls and sprinkle with chopped cilantro. Serve immediately.