Begin by making the andouille hash: Fill a three quart saucepan with water and heat it to boiling. Add some salt and the potatoes and boil until they're fork tender, about 15 minutes. Drain.
Preheat the oven to 350 degrees.
In a small bowl, stir together the spice mix: the paprika, garlic powder, oregano, salt, cayenne, and thyme.
In a cast iron skillet, melt the butter on high heat. Dip both sides of the salmon in the spices ( but reserve a a half teaspoon for the hash). Cook until brown on both sides and then put in a buttered baking dish and bake for about ten minutes, or until it's cooked through.
Make the roasted garlic aioli: In a cast iron skillet, in a tablespoon of oil until they're brown and tender. Put them in a small bowl, and mash them into a paste. Add the mayonnaise, white wine, black pepper, and Dijon mustard.
Heat a large skillet on medium heat. Cook the onions and peppers until they're tender in a the olive oil. Add the potatoes, andouille, and a half teaspoon of the spices, and cook on medium heat for about ten minutes.
Serve the salmon with the hash and aioli.