In a small bowl, mix the brown sugar, smoked salt and 1 tbsp. smoked paprika. Sprinkle some of the smoked-salt mixture inside the turkey cavity and the remaining mixture evenly all over the turkey. Cover; refrigerate overnight.
Preheat the oven to 400°. Place the turkey on a rack set inside a large roasting pan; place the apple and onion in the cavity of the turkey. Pour 1 cup water into the roasting pan. Brush the turkey with some of the melted butter. Roast the turkey 30 minutes. Reduce the oven temperature to 350° and continue roasting, occasionally brushing with more melted butter, rotating the pan every half hour and tenting with foil if browning too quickly, and adding more water to the pan if needed, until an instant-read thermometer inserted into the thickest part of the thigh (not touching bone) registers 165°, 2 to 2 1/2 hours. Let rest about 15 minutes. Carefully tilt the turkey so the juices from the cavity pour into the pan. Transfer the turkey to a platter. Let rest at least 15 minutes more.
In a small bowl, whisk 1/2 cup stock and the flour until smooth. Using a large spoon, skim off some of the fat from the juices in the roasting pan; discard. Add the cider, the remaining stock and the flour mixture to the roasting pan. Place the pan over two burners on the stove. Bring to a boil over medium-high heat, whisking and scraping up browned bits from the bottom of the pan; reduce the heat to medium and simmer, whisking often, until the gravy thickens, about 10 minutes. Stir in the vinegar and season the gravy with salt and pepper. Strain, if desired.
Carve the turkey and serve with the gravy.