2 tablespoons vegetable oil, divided
1 small yellow onion, halved through root
1 bunch small baby turnips (about 12 oz.), greens torn into pieces, turnips peeled, quartered
3 large shallots, sliced into rings
1 3” piece ginger, peeled, sliced ¼” thick
3 oz. kombu
1 tablespoon kosher salt, plus more
1 cup dry vermouth
½ small butternut squash (about 12 oz.), peeled, seeded, cut into ½”-thick pieces 6 4-oz. pieces
skin-on salmon fillet
Freshly ground black pepper
1 lemon, halved
Heat 1 Tbsp. oil in a large skillet over medium-high heat. Add onion, cut sides down, and cook, undisturbed, until dark brown, about 5 minutes.Transfer onion to a large Dutch oven or other large pot and add turnips, shallots, ginger, kombu, 1 Tbsp. salt, and 8 cups water. Bring to a gentle simmer (do not boil or broth will be bitter) and cook until broth is light golden and onion is soft, 40–50 minutes.Add vermouth to broth and simmer 5 minutes. Remove onion and kombu, discard. Add squash and simmer until just softened, 12–15 minutes. Add turnip greens and simmer, stirring occasionally, until tender, about 2 minutes. Meanwhile, season salmon with salt and pepper. Heat remaining 1 Tbsp. oil in a large skillet over medium-high heat. Cook salmon, skin side down, until skin is very crisp, about 2 minutes. Turn salmon and cook 30 seconds longer (salmon will be rare; it will continue to cook in the hot broth). Spoon broth and vegetables into shallow bowls and top with salmon, skin side up; squeeze lemon over.
DO AHEAD: Broth and vegetables (without turnip greens) can be made 1 day ahead. Reheat and add greens just before serving.