Thaw fish, if frozen. Rinse the fish; pat dry with paper towels. Sprinkle with pepper and salt. Measure thickness of fillets. Cook the salmon in hot oil in a large nonstick skillet over medium heat for 4 to 6 minutes per ½-inch thickness or until the salmon flakes easily when tested with a fork, carefully turning once halfway through cooking. Remove from the skillet and keep warm.
Add mushrooms and shallot to the same skillet. Cook for 3 to 5 minutes over medium heat or until tender, stirring occasionally. Remove from heat and carefully add wine, mustard, and thyme. Cook and stir for 1 to 2 minutes or until well combined and heated through.
Place the salmon on serving plates and top with the mushroom sauce.