Cook pasta in boiling water according to the package directions. Drain, reserving pasta water. Toss pasta with 1 teaspoon olive oil. Keep it warm.
Heat 2 tablespoons olive oil in a large saucepan over medium heat. Add the onions. Cook and stir until softened. Add red pepper flakes, oregano, and salmon. Break up the salmon with a spatula as it cooks. Stir in dill, chopped tomatoes, and wine; bring to a boil. Turn heat to low. Simmer for 10 minutes; season with salt and pepper. Add some reserved pasta water if the sauce gets dry.
Mound the pasta on plates. Make a well in the center of each mound and ladle in the tomato-salmon sauce. Garnish with parsley and Parmesan cheese. Serve warm.