Remove neck and giblets; reserve for other uses. Remove and discard excess fat. Rinse the bird inside and out and pat dry. Season body cavity with salt and pepper. Tie legs together and twist wing tips under back. Brush turkey with oil and lightly sprinkle with salt and pepper. Arrange turkey breast side up, in center of cooking grate. Place lid on grill. Cook 11 to 13 minutes per pound or until an instant read thermometer inserted into the thickest part of the thigh not touching bone registers 180 degrees and the juices run clear. Transfer turkey to a platter. Let stand for 15 minutes before carving.
Combine turkey neck and giblets in a saucepan and cover with water. Bring to a boil and simmer 15 minutes, skimming. Add bouquet. Simmer 20 minutes. Remove stock from heat and strain. Reduce to 3 cups if necessary. Have a roasting pan with 6 tablespoons turkey fat. Add flour to fat and cook for 3 minutes. Add wine to roux and whisk until smooth. Add stock and bring to a boil.
Recipe courtesy of Weber Grills