Whisk broth, coconut milk, and curry paste together in a 4-qt. pot. Heat over high heat until boiling. Add ginger, sugar, and lime juice, then reduce heat to a simmer. Add rau ram and sprouts and cook 2 minutes.
Remove from heat and add seafood. Stir gently to combine and let residual heat cook fish until opaque, 3 to 5 minutes.