Heat oil in a large saucepan or Dutch oven over medium heat. Add carrot and celery and cook, stirring frequently, until the vegetables just begin to brown, 3 to 4 minutes. Add broth, water, salmon, cauliflower and chives (or scallions) and bring to a simmer. Cover and cook, maintaining a gentle simmer, until the salmon is just cooked through, 5 to 8 minutes. Remove the salmon to a clean cutting board. Flake into bite-size pieces with a fork.
Stir instant potatoes (or leftover mashed potatoes), dill (or tarragon) and mustard into the soup until well blended. Return to a simmer. Add the salmon and reheat. Season with salt and pepper.