Preheat the grill to low heat. Using heavy-duty aluminum foil, make two 1-cup packets of smoke chips. Poke holes in one side of each packet to create vents.
In a spice grinder, combine the ancho powder, caraway seeds and dried onion with 1 1/2 teaspoons of kosher salt and 1/2 teaspoon of ground pepper and pulse until finely ground. Transfer to a small bowl and stir in the butter. Reserve 3 tablespoons of the seasoned butter for the gravy.
Starting from the neck end of the turkey, slip your hands between the skin and flesh, being careful not to tear the skin. Slip your hands as far down the legs as possible. Rub half of the remaining butter under the skin of the turkey and place the bird, skin side up, in 3 stacked sturdy disposable roasting pans. Rub some of the remaining butter over the skin.
Place one of the chip packets directly on the heat source and replace the grate. Set the roasting pans on the grate. Cover and grill the turkey for 1 hour, basting occasionally with the remaining butter.
Place the second chip packet on the grill. Using 2 pairs of tongs, carefully transfer the turkey to the grill, skin side up. Turn off one of the burners and grill over low heat, turning the turkey twice, until an instant-read thermometer inserted in the thigh registers 175°, about 1 1/2 hours longer.
Pour the pan juices into a heatproof measuring cup; skim off the fat (there should be 1 cup of juices). In a saucepan, melt the reserved 3 tablespoons of seasoned butter. Whisk in the flour, then whisk over moderate heat for 2 minutes. Whisk in the stock and pan juices and bring to a boil; simmer over moderate heat until thickened.
Carve the turkey and serve with the caraway-ancho gravy.
The seasoned butter can be frozen for up to 1 week.
Ask your butcher to remove the backbone and crack the breastbone so the turkey will lie flat on the grill.