In a heavy bottom, large saute pan over medium heat, add 2 tablespoons of extra virgin olive oil. Sprinkle sliced onions with a little sea salt and add to the olive oil, stirring occasionally, until golden brown, about 5 minutes. Add the wild mushrooms and rosemary leaves, (discarding any woody stems). Saute until both the mushrooms and onions become deep golden brown and caramelized. Add the balsamic to the pan with the mushrooms and onions and de-glaze. Simmer gently and cook until the balsamic is reduced by half. Add the cream, and stir to combine. Cook until the mixture thickens slightly, approximately another minute. Season with salt and pepper to taste and reserve.
Lightly score the salmon skin in several places with a sharp knife without penetrating the flesh. Pat the fillets dry and season with salt and pepper to taste. In a pan large enough to hold the fillets, heat 2 tablespoons of extra virgin olive oil over medium high heat. Pan sear the fillets, for approximately two minutes per side, taking care not to overcook.
Serve the salmon with the balsamic-mushroom sauce over the top. Can be accompanied by pasta, quinoa or brown rice.