Step 1
The night before roasting dissolve salt and sugar in 3 gallons of cold water in a large clean ice chest or similar container in a cold spot such as an unheated basement or garage. For those in warm climates add ice packs to keep turkeys cool. Add turkeys breast-side down; cover and let stand about 12 hours. (This brining keeps the turkey from drying out and seasons it right down to the bone.) Drain. Rinse turkeys and pat dry.
Step 2
About five hours before serving set oven to 425 degrees and adjust oven rack to lower-middle position. Place turkey No. 1 breast-side down and cut out the back with kitchen shears. Open up turkey and turn it breast-side up pressing on it with your palms so it lies flat. Place turkey skin-side up on a lipped cookie sheet over a bed of half the chopped vegetables. Brush turkey with butter.
Step 3
Roast until a meat thermometer inserted into the thigh registers 175 degrees 1 to 1 1/2 hours. Watch vegetables and pan drippings throughout - they should be kept dry enough to brown and produce the rich brown goo with which to brush Turkey No. 2 and make a rich gravy but moist enough to keep from burning. So add water as needed throughout the cooking.
Step 4
Remove pan from oven and transfer turkey to a cutting board; reserve vegetables and pan juices for Turkey No. 2. Let the bird rest 30 minutes to 1 hour before carving to allow the meat to firm up. Carve transferring slices to an ovenproof serving platter or baking pan. Cover with aluminum foil. Refrigerate or set in a cool spot (below 40 degrees) until mealtime. Gently rewarm covered on platter or baking pan.
Step 5
Immediately after removing the first turkey lower the oven temperature to 400 degrees and adjust oven rack to lowest position. Scrape vegetables and pan drippings from Turkey No. 1 into a roasting pan. Set a V-rack in the pan. Place remaining raw vegetables in the cavity of Turkey No. 2 then tie legs together with kitchen string for a nicer presentation. Set turkey breast-side down on rack. Brush with pan drippings from Turkey No. 1.
Step 6
Roast 1 hour. Remove from oven; baste back and sides with pan drippings. Using two wads of paper towels carefully turn breast-side up and baste. Keep roasting until a thermometer inserted into the leg registers 175 degrees 1 to 1 1/2 hours longer. Again watch vegetables and drippings throughout and add water as needed. Transfer turkey to a platter for display (and then for seconds and leftovers).
Step 7
For gravy: Set roasting pan over 2 burners on medium-high heat. Add wine and using a wooden spoon stir to loosen brown bits. Strain contents of pan through a large strainer into a saucepan. Add broth and bring to a boil. Whisk cornstarch with 1/2 cup water (or 1/2 cup flour with 1 cup water) then gradually whisk into pan juices. Bring to a boil reduce heat to low and simmer until thickened. Serve immediately.