Salmon. Pat salmon (1 pound) dry with paper towels and sprinkle with salt and pepper on both sides. Heat 1 tablespoon of oil in a large pan over medium heat. Sear salmon (skin side first) on each side until golden brown, about 4 minutes. Set cooked salmon aside on a clean plate tented with foil.
Sauce. Add the remaining tablespoon of oil to the pan, along with the shallots (2), and cook until softened, about 4 minutes. Add wine (1/3 cup) and scrape up any bits from the bottom of the pan. Add chicken broth, lemon juice (1 1/2 tablespoons), and lemon slices (1/2) and bring sauce to a simmer. Cook until the sauce thickens enough to coat the back of a spoon. Once thick, remove from heat, and add the butter (1 1/2 tablespoons), capers (1 tablespoons), and parsley (1 tablespoons). Taste and adjust seasoning to your liking.
Assemble. Place 1 salmon filet on each plate and spoon sauce on top. Sprinkle with additional parsley, and enjoy!