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 lime juice. Return to a simmer and cook until thickened, about 7 minutes. Remove from heat and set aside.
In a medium bowl, stir together the bread crumbs, 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.
