Special equipment: a pressure cooker or stockpot; a syringe or brining needle
For the stock: Preheat the oven to 375 degrees F. Lightly butter a roasting pan and add the turkey parts in a single layer. Roast until golden brown, 20 to 25 minutes. Cool completely in the pan.
Put the roasted turkey in a pressure cooker with the onion, carrot, celery, garlic, soy sauce and 8 cups water. Lock the lid in place, put over high heat, and bring the cooker to high pressure. Lower the heat to maintain high pressure and cook 15 minutes. Remove from the heat. Let the pressure dissipate naturally, about 2 minutes, or according to the manufacturer's instructions. Remove the lid and skim the stock.
Alternatively put the roasted turkey pieces, the onion, carrot, celery, garlic, soy sauce and 8 cups of water in a stockpot over high heat. Bring to a simmer, reduce the heat to low, and simmer, skimming occasionally, for 2 hours. You should end up with about 8 cups of stock.
Strain the stock through a fine sieve. The stock may be used immediately or cooled and refrigerated for at least 4 hours and up to 24 hours. If refrigerated, the fat will congeal on the top of the stock and should be removed before continuing.
For the brine: Put 1 cup of the turkey stock, the mayonnaise, garlic, lemon juice, thyme, coriander, fennel, salt and mustard seeds in a blender and blend until smooth, about 1 minute. Strain, discarding the solids. Reserve the remaining stock for another use.
For everything else: Using a syringe or brining needle, inject the brine into the turkey breast in multiple spots so it is evenly distributed throughout the meat. Roast immediately, or cover with plastic wrap and refrigerate for up to 8 hours; bring to room temperature before roasting.
Preheat the oven to 400 degrees F. Put the broccoli rabe and onions in a roasting pan. Put the turkey breast on top, rub with the olive oil to coat, and season with salt and pepper. Pour the apple cider into the bottom of the pan.
Roast the turkey, basting occasionally, until the skin is golden brown and a meat thermometer inserted in the thickest part of the breast reads 165 degrees F., about 2 hours. Remove from the oven and let rest for 15 minutes.
Transfer the turkey to a cutting board. Put the broccoli rabe, onions and any pan juices on a serving platter. Slice the turkey, arrange it over the vegetables and serve family-style.