Adjust oven rack to middle position and preheat oven to 450°F. Scatter the vegetables and sage on the baking sheet. Set aside.
To spatchcock the bird, place it in the sink, breast side down. Using poultry shears, cut lengthwise on both sides of the backbone from the neck to tail. Remove the backbone and place it in the simmering stock. (I also add the neck that usually is inserted into the cavity of the bird as well as the onion skins and carrot peels.)
Flip the bird over and press firmly with both hands to flatten the bird. Season turkey liberally on all surfaces with salt and black pepper. Transfer the bird to the prepared baking sheet. Tuck the wing tips under the bottom of the bird and arrange the drumsticks so that they are not askew for the best presentation. Season the top of the turkey with paprika.
Transfer the baking sheet to the oven and roast, rotating occasionally, until an instant read thermometer inserted into the deepest part of the breast registers 150°F, and the thighs registers 165°F, about 80 minutes.
While turkey roasts, start the gravy. Strain the broth, discarding the bones and onion skins. Melt butter over medium-high heat in a saucepan. Add flour and cook, stirring constantly until flour is golden brown, about 3 minutes. Whisking constantly, add the strained broth in a thin, steady stream until it it all incorporated. Add apple cider and apple cider vinegar. Bring to a boil, reduce to a simmer, and cook until reduced to about 1 quart, about 20 minutes longer. Season to taste with salt and pepper, cover, and keep gravy warm.
When turkey is cooked, remove from oven and allow to rest at room temperature for 20 minutes before carving. Transfer it to a cutting board set over a 2nd rimmed baking sheet to catch the juices; cover the bird with foil.
Remove the vegetables from the baking sheet with a slotted spoon, discarding any sage leaves. Carefully pour any collected juices from out of the roasting pan through a fine-mesh strainer into a liquid measuring cup. Skim off excess fat.
Add defatted cooking juices and to the gravy. At this point for the vegetables you have choices. A) add the vegetables to the gravy and puree with an immersion blender. B) Serve them as a side dish. Discard is not a choice! Regardless, simmer until the gravy coats the back of a spoon. Taste and adjust for seasoning with salt and pepper. Keep warm.
Remove the foil from the bird and carve. (See below) Transfer to a warmed serving platter.
Transfer the sliced meat, meat, and wings to the warm serving platter. Serve immediately with gravy on the side.