Saute green onions and celery in 1 tbsp butter in a skillet over medium-high heat, stirring constantly, until tender. Set aside.
Remove and discard skin and bones from salmon, if desired. (I usually remove the skin, but crush up the bones to retain the calcium). Combine salmon, reserved green onion mixture, egg, and next 5 ingredients. Shape mixture into 4 patties. (Mixture will be very sticky). Dredge in flour. Cook in 1/4 cup melted butter in a skillet over medium heat 5 minutes on each side or until browned. Serve patties with the warm mushroom sauce.
Saute mushrooms in butter in a large saucepan over medium-high heat, stirring constantly, until almost tender. Add the minced garlic, and cook 1 minute longer. Remove mushrooms and garlic from the saucepan, reserving drippings in the pan. Reduce the heat to low.
Add 1 tbsp flour to the drippings, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add half-and-half, wine, soy sauce, and lemon-pepper seasoning; cook over medium heat, stirring constantly, until thickened and bubbly. Return mushrooms to pany; cook until heated.