Place chicken, breast side down, on cutting board. Using kitchen shears, cut through bones on either side of backbone; discard backbone. Do not trim off any excess fat or skin. Flip chicken over and press on breastbone to flatten.
Sprinkle salt liberally all over the chicken and under the skin. Refrigerate overnight, uncovered.
When ready to roast, adjust oven rack to middle position and preheat oven to 475 degrees. Toss bread with stock and 2 tablespoons olive oil until pieces are evenly moistened. Arrange bread in an ovenproof skillet in a single layer (I used a cast iron pan).
Pat chicken dry with paper towels and place, skin side up, on top of bread. Brush chicken skin with oil, then salt and pepper liberally. Roast chicken for 40-45 minutes, turning the skillet halfway through.
While the chicken and bread roast, make the dressing by whisking vinegar and mustard together. Slowly whisk in ¼ cup oil. Stir in scallions and currants. Add salt and pepper to taste, then set aside.
Transfer chicken to carving board and let rest for 15 minutes. Carve chicken and add any drippings to the vinaigrette. Add bread and vinaigrette to arugula in a large bowl and toss to coat. Transfer salad to a serving platter and top with the carved chicken pieces.