Brown the turkey:
Preheat the oven to 325°F. Combine the flour, salt, pepper, sage, and thyme in a large bowl; remove and reserve ⅓ cup of the seasoned flour. Dredge each piece of turkey in the flour mixture, shaking off the excess; arrange on a plate. Heat the oil in the Cravings braiser over medium heat. Working in batches if necessary, brown the turkey thighs, flipping once midway through, making sure not to burn the flour, 10 minutes total. Transfer the turkey to a plate, leaving the drippings in the pan.
Cook the veggies and braise turkey:
Add the butter to the braiser, then add the onions, carrots, celery, garlic, sage, and thyme to the skillet and cook, stirring, until the vegetables begin to soften, 5 minutes. Add 2 tablespoons of the reserved seasoned flour to the vegetables and cook, stirring, until absorbed, 2 minutes. Return the turkey to the braiser, add the stock (it won’t completely cover the turkey but will come up about ¾ of the way up the turkey), bring to a boil, cover with the lid, and carefully transfer to the oven. Cook the turkey until the meat is tender and falling off the bone, 3 hours.
Make the gravy:
Using tongs, remove the turkey pieces to a plate. Place the remaining 3 tablespoons seasoned flour into a bowl, then whisk in 1 cup of the hot braising liquid until smooth, and whisk back into the braiser. Bring the liquid to a boil, then reduce the heat to medium heat and cook, stirring, until thickened and reduced for 20 minutes.
Make the potatoes:
While the gravy is thickening, place the potatoes in a large pot, cover with 2 inches cold water, bring to a boil, then reduce the heat to medium and cook until the potatoes are fork-tender, 22 to 23 minutes. Drain, transfer to a bowl, then add the butter with the cream cheese, parmigiano reggiano, salt, and pepper and use an electric hand mixer to whip the potatoes just until smooth, 1 minute.
Add turkey back in and top with potatoes:
Pull the cooled turkey from the bones, discard the bones and skin, and tear the turkey into bite-sized chunks. Return the turkey to the pan, stir to incorporate with the gravy, add the parsley, and season with salt and pepper to taste. Raise the oven temperature to 400°F. Top with the mashed potato mixture, forming decorative peaks if you like. Transfer the braiser to the oven and bake, uncovered, until the top is golden, 25 to 30 minutes. Remove from the oven, cool for 10 minutes, then spoon onto plates or into bowls.
