Heat the vegetable oil and sesame oil in a large skillet over medium heat.
Add the green onion and garlic, and cook until tender.
Stir in the miso paste and sake until blended.
Bring to a simmer then stir in the cream and limejuice.
Return to a simmer and cook until thickened, about 7 minutes.
Remove from heat and set aside.
In a medium bowl, stir together the breadcrumbs, salmon, onion, and cilantro.
In a small bowl, whisk together the egg, soy sauce and water using a fork.
Stir about half of this into the salmon mixture, and if it seems dry, stir in a little more until the salmon mixture will stick together in patties.
Heat the oil in a large skillet over medium-high heat.
Form the salmon mixture into 2-inch patties for appetizers, or 4-inch patties for a main dish.
Fry patties for about 4 minutes per side, or until golden brown.
Serve with the sauce drizzled over, or separately for dipping.
Ready in 30 min.