Place a large cast-iron or other ovenproof skillet in a cold oven. Preheat oven to 450°. Meanwhile, brush salmon with oil and sprinkle with salt and pepper.
Carefully remove skillet from oven. Place fish, skin side down, in skillet. Return to oven; bake uncovered, until salmon flakes easily and a thermometer reads 125°, 14-18 minutes. Cut salmon into 4 equal portions.
FOR GREMOLATA: In a small bowl, mix 1/4 cup minced fresh parsley, 2 tablespoons olive oil, 1 tablespoon lemon juice, 1 minced garlic clove, 1 teaspoon grated lemon zest, 1/2 teaspoon salt and 1/4 teaspoon pepper. FOR DILL AND CAPER BUTTER: In a small bowl, mix 1/4 cup softened butter, 1 tablespoon minced shallot, 1 tablespoon minced fresh dill, 1 teaspoon Dijon mustard and 1 teaspoon chopped capers. FOR MAPLE SOY GLAZE: In a small bowl, mix 1/4 cup maple syrup, 2 tablespoons soy sauce, 1 minced green onion, 1/2 teaspoon grated fresh ginger and 1/4 teaspoon red pepper flakes.