Place salmon scraps in a large pot and cover with water. Bring to a boil, then reduce heat and simmer for 60-90 minutes, skimming off any foam that rises to the surface.
Strain the stock, reserving the liquid. Discard the solids. Pick any remaining meat from the solids.
Roast the red bell pepper until charred. Peel and remove seeds.
In a clean pot, combine the salmon stock, salvaged meat, and roasted red pepper. Bring to a simmer.
Add the chives to the soup. Blend with an immersion blender until smooth.
Stir in the heavy cream and season with salt and pepper to taste.
Strain the soup through a fine-mesh sieve. Reserve the fish paste.
Stir some of the reserved fish paste back into the soup for added flavor and thickness (optional).
Serve the soup garnished with dill oil, pea sprouts, and chopped green onion.