To salt the chicken overnight, begin by removing any strings and pat dry. Sprinkle generously with kosher salt and set on a plate. Cover loosely with cling film and refrigerate overnight. Otherwise, proceed with the recipe.
Preheat the oven to 400°F. Place the chicken on a rack in a roasting pan. Pat the chicken dry. Rub a little olive oil over the chicken. Tuck the wing tips under the bird. Roast the chicken for 1 to 1 ¼ hours until fully cooked to an internal temperature of 165°F.
Bring a large pot of water to a boil. Season the water with kosher salt and add the baby potatoes. Cook the potatoes just until they are fork-tender. They should be cooked through but not falling apart. Drain the potatoes and let cool briefly.
To smash the potatoes, lightly brush a baking sheet with olive oil. Spread the cooked potatoes out evenly on the baking sheet. Using the bottom of a glass, or your palm, press down to smash the potato. Repeat with the remaining potatoes.
In a small bowl stir together the minced garlic and 4 Tbsp olive oil. Brush the smashed potatoes with the garlic oil. Sprinkle with kosher salt and pepper. Bake alongside the chicken at 400°F for 25 to 30 minutes until browned and crispy. Let cool briefly before assembling.
To make the dressing, combine the finely diced shallot, Dijon mustard, dry vermouth, sherry wine vinegar, 1/4 tsp kosher salt, and a pinch of pepper in a small bowl. Whisk together. Slowly drizzle in the light olive oil whisking constantly to emulsify. Add the chopped fresh tarragon.
Once the chicken reaches an internal temperature of 165°F take out of the oven and transfer the chicken to a plate. Spoon the fat off the drippings in the roasting pan. Discard the fat and save the drippings in the pan.
Place the roasting pan on the stove over medium heat. When the drippings begin to sizzle add 3 tablespoons of the tarragon vermouth dressing. Use a wooden spoon to scrape up all the brown bits on the roasting pan. Pour the pan drippings into a bowl.
Carve the chicken by removing and separating the legs. Remove the breasts and cut into thick slices. Remove the wings. See above for more detailed instructions.
To assemble the dish, toss the salad greens with some of the tarragon vermouth dressing. Drizzle any extra dressing over the smashed potatoes. Layer the potatoes with the dressed greens on a serving platter or individual plates. Arrange the chicken pieces around the salad. Spoon the pan drippings over the chicken and salad. Enjoy!