Heat 1 tablespoon oil in a skillet over medium heat and cook shallots until soft and translucent, about 2 minutes. Stir in curry paste, coconut milk, chicken broth, and sugar. Bring to a simmer, reduce heat to low and cook until curry has reduced by half, about 10 minutes. Season with salt if necessary.
Season fish with salt and carefully place in the skillet with the curry sauce, spooning some curry sauce on top. Cover skillet and cook until fish flakes easily from fork and is cooked through, about 5 minutes. Remove fish from skillet.
Stir cilantro, green onions, and lime juice into curry sauce and serve with the fish. Serve with lime wedges.
