Cut 1 orange into quarters and add to the pan with the turkey.
Cut 1 medium onion into quarters and add to the pan with the turkey.
Add 2 bay leaves to the pan with the turkey.
Add enough water to cover the turkey halfway.
Cover the pan and bring to a boil over high heat.
Reduce the heat to a bare simmer and braise until the turkey is fall-off-the-bone tender, 45 minutes to 1 hour.
At this point, everything can be refrigerated overnight for use the next day.
Carnitas
Discard the orange, the onion, and the bay leaves.
If the turkey has not been refrigerated, drain the turkey well.
Shred the turkey and discard the bones.
If the turkey has been refrigerated, warm it in a cast iron or nonstick skillet over medium-low heat until the gelatinous braising liquid becomes liquid again, and drain the turkey well. Rinse and dry the skillet for further use.
Heat fat in a cast iron or nonstick skillet over medium-high heat until shimmering.
Add the turkey and spread into an even layer.
Cook, without moving, until meat is well browned and crisp on the bottom, about 5 minutes.
Stir turkey to incorporate the crisp bits and introduce new soft bits to the bottom.
Continue this process until the turkey is as crisp as you prefer.
Season with salt.
Notes
1 pound of leftover dark-meat turkey means 1 pound of just the meat. Remove the skin from the legs and thighs, remove the meat from the bones, use 1 pound of meat in the recipe, and then throw in all of the skin and bones.