For the turkey: Preheat the oven to 300 degrees F. Sprinkle the turkey breast liberally with salt and pepper. Rub with the brown sugar and chopped thyme. Wrap in aluminum foil and roast in the oven until the meat has reached an internal temperature of 160 degrees F, 4 to 5 hours. Remove from the oven and let cool completely before opening and slicing.
For the confit: Lower the oven temperature to 200 degrees F. Warm the duck fat in a large pan big enough to hold the legs and thighs. Rub the legs and thighs with salt, and then submerge in the duck fat. Add a sachet of the thyme and the bay leaves to the fat. Cover with aluminum foil and roast until the meat is tender and pulls away effortlessly with a fork, 6 to 8 hours. Remove and let cool in the duck fat overnight.
Gently warm the turkey confit, just enough to remove the turkey from the fat. Shred the meat into pieces and toss with a little bit of the reserved fat. Reserve some more of the fat for assembling the sandwiches.
Press the confit into a baking dish or small baking tray in a single 1/2-inch layer. Lay plastic wrap over the tray directly touching the confit, and place another tray on top. Add a few cans or weights to press it down and let it sit overnight.
Unwrap the confit and cut 1 square per sandwich about the same size as the bread slices. Toast the bread, and then slice the turkey breast very thinly across the grain.
Heat 2 tablespoons of duck fat in a nonstick pan over medium heat until hot. Place the squares of confit in the pan and fry until brown and crisp on both sides. Spread mayonnaise evenly over the bread slices. For each sandwich, place the confit on one slice and top with another piece of bread. Add 4 slices bacon, some tomato, turkey breast and lettuce. Top with last piece of bread and serve.