In a sauté pan, heat 1 tablespoon olive oil. When the oil is hot, add the Andouille sausage and render for 3 minutes. Add the onions and sauté for 2 minutes. Add the garlic and potatoes and sauté for 1 minute. Season with salt and pepper. Add the veal reduction and green onions. Bring the liquid up to a boil. Reduce the sauce to a simmer and cook for 3 to 4 minutes. Remove from the heat and keep warm. Season the salmon fillets with salt and pepper. In a sauté pan, heat the remaining olive oil. When the oil is hot, sear the salmon for 2 minutes on each side. Remove the pan from the heat and brush each fillet with a tablespoon of the barbecue sauce. Place the pan in the oven and roast for 2 to 3 minutes for medium rare. Season the flour with salt and pepper. Dredge the onions in the seasoned flour. In a sauté pan, heat the vegetable oil. When the oil is hot, add the onion rings and fry until crispy and golden brown, about 2 to 3 minutes, stirring constantly. Remove from the oil and drain on a paper-lined plate. Season the onions with salt and pepper. To assemble, spoon about 1/4 cup of the barbecue sauce in the center of each plate. Spoon 1/2 cup of the hash in the center of the sauce. Lay the salmon fillet directly on top of the hash. Garnish with the fried onions and parsley.