Heat oven to 325°F. Season turkey with salt and pepper and brown in oil in a Dutch oven over medium-high heat for about 3 minutes per side.
Lift turkey out, soften onion in the pot for 5 minutes, then add cider, 2 cups stock and sage. Return turkey, cover and braise in the oven for 1 3/4 to 2 1/4 hours until at least 175°F and tender enough to pull from the bone.
Rest turkey for 10 minutes. Remove all bones and firm connective tissue and pull the meat into broad pieces.
Strain the braising liquid, discard spent onion and skim the fat. Measure 2 cups, adding from the reserved stock only if needed to reach that amount.
Melt butter in a saucepan and stir in flour for 1 minute. Whisk in the measured liquid and simmer for 5 minutes until the gravy lightly coats a spoon.
Fold turkey into the gravy and heat gently to 165°F. Toast the bread on both sides under the broiler for 1 to 2 minutes total.
Set one toast slice on each plate, divide turkey over it and spoon gravy over the meat. Serve the four open-faced sandwiches immediately with a knife and fork.