Make the potatoes: Preheat the oven to 350 degrees F. Toss the potatoes with 1 tablespoon olive oil and a generous pinch of salt. Arrange on a baking sheet; bake 35 to 40 minutes, or until tender when pierced with the tip of a knife. Remove and let cool.
Increase the oven temperature to 375 degrees F. In a cast-iron skillet, heat the remaining 3 tablespoons olive oil over medium heat until hot. On a flat surface, smash and break the potatoes with the back of a wooden spoon. Season with salt. Add to the skillet and cook until browned (do not stir them!), 4 to 5 minutes. Flip the potatoes and cook 3 to 5 additional minutes. Season with salt and sprinkle with the red wine vinegar.
Meanwhile, make the salmon: Line a rimmed baking sheet with foil; drizzle with 1 tablespoon olive oil. Arrange the salmon skin-side down on the baking sheet. Dot with the butter and drizzle with the remaining 1 tablespoon olive oil. Season thoroughly with salt. Use a fine-mesh strainer to sprinkle the cayenne over the fish. Bake, undisturbed, 6 to 8 minutes. (For well-done, bake an additional 5 minutes.) Remove from the oven.
Make the salad: Toss the parsley, tarragon, arugula and radishes. Serve the salmon and potatoes with the herb salad. Squeeze the lemon juice over the fish.
Photograph by Ryan Liebe
Recipe courtesy of Alex Guarnaschelli for Food Network Magazine