Place fish fillets, skin sides up, on a wire rack set inside a rimmed baking sheet. Chill, uncovered, at least 1 hour or up to 8 hours or overnight. Process scallion greens, watercress, 1/4 cup fresh herbs, mayonnaise, sour cream, 1 tablespoon lemon juice, 1 tablespoon water, anchovies, and 1/4 teaspoon salt in a blender until smooth, about 30 seconds. Cover and chill until ready to serve. Preheat oven to 500°F with rack in lowest position. Season both sides of fillets with 1 1/2 teaspoons salt. Heat 1 tablespoon oil in a large cast-iron skillet over medium-high until a wisp of smoke forms. Lay 1 fillet, skin side down, in skillet, and immediately press down on fillet evenly and with firm pressure using a stiff spatula; press 30 seconds. Check the skin by gently lifting a corner of the fillet; if it needs a little more time to begin lightly browning around the edges, cook an additional 15 seconds. If skin sticks, add 1/2 tablespoon butter to skillet, and gently lift the corner of the fillet while tipping the skillet so the butter flows under the fish. Once the fillet is lightly browned around the edges, transfer it, skin side up, to a plate. If butter was added, wipe skillet clean, and add 1 tablespoon oil. (If no butter was used, don’t wipe skillet clean or add any more oil.) Repeat process 3 times using remaining fillets. If butter was used in step 4, wipe skillet clean, and add 1 tablespoon oil. Return all fillets to skillet in a single layer, skin sides down. Transfer skillet to lowest rack or the deck of preheated oven; cook according to fillet thickness, about 8 minutes per inch. Use a metal skewer or cake tester to pierce the meat at its thickest point; when removed, it should feel quite warm when pressed to your lip. For an additional test, fleck a bit off the meat that you will serve yourself; fish will flake when it is done. Cover with aluminum foil to keep warm. Heat remaining 1 tablespoon oil in a large skillet over medium. Cut a 1-inch-long slit through the core of each lettuce head half. Add lettuce and remaining 1/2 teaspoon salt to skillet; cook, tossing occasionally, until wilted, about 2 minutes. Reduce heat to medium-low, and add broth; cook, tossing occasionally, until lettuce is tender, 2 to 4 minutes. Spread dressing evenly on 4 plates. Top evenly with braised lettuce, fish fillets, hazelnuts, and remaining 1/4 cup fresh herbs. Drizzle fish with remaining 1 tablespoon lemon juice. Serve immediately.