Place the chicken in a baking dish. Using your fingers, gently loosen the skin from the breasts and thighs without breaking the skin. Carefully slide the sprigs of thyme and the garlic under the skin. Put the lemon in the cavity. Tie the legs together and tuck the wings under the body. Sprinkle with 2 teaspoons of sea salt and the pepper, cover the dish tightly with plastic wrap, and refrigerate for 24 to 48 hours.
Preheat the oven to 500 degrees F. (Be sure your oven is very clean!) Place the bread in a medium (10-inch) cast-iron skillet in a single layer. Brush the chicken with olive oil and place it, breast side up, on top of the bread. Roast for 30 minutes, turn it over and roast for 15 minutes, until the juices run clear when you cut between the leg and the thigh. Wrap the skillet tightly with aluminum foil and allow the chicken to rest at room temperature for a full 30 minutes. (Don¿t worry; it will stay hot.) The bread will be almost burnt on the bottom and soft with the pan drippings on top.
Place the Arugula Salad in a very large, shallow serving platter. Put the chicken and the bread on a cutting board. Cut the bread into 1-inch squares and sprinkle them on the salad. Carve the chicken thickly (see note) and place it on top of the salad. Spoon the pan juices over the chicken, sprinkle it with sea salt, and serve warm.
Whisk the vinegar, mustard, garlic, 1 teaspoon salt, and 1/2 teaspoon pepper together in a small bowl or glass measuring cup. Whisk in the olive oil, stir in the scallions and currants, and set aside.
Place the arugula in a large bowl, add the vinaigrette, and toss well.
To carve, cut off the legs and cut between the thigh and the leg. For the breasts, cut the wings off, remove each breast in one large piece, and make thick slices crosswise.