Season turkey fillet on both sides with salt and pepper. Heat oil in a large, heavy-bottomed skillet over medium high heat. Add turkey and cook for 2 minutes. Reduce heat to medium and cook for another 8 minutes, or until turkey is golden brown. Flip and continue cooking until turkey is just cooked through, about 10 minutes more. Transfer to a plate and set aside.

Melt butter in the same skillet, then whisk in flour until a paste forms. Cook, continuing to whisk constantly, until light brown and fragrant, about 1 minute. Carefully whisk in broth until smooth, scraping up all the browned bits from the bottom of the skillet. Season with salt and pepper, then reduce heat to a simmer and cook until gravy thickens, about 5 minutes. Meanwhile, thinly slice the turkey and transfer it to the skillet with the gravy to warm through.

Spread some of the cranberry sauce on each slice of bread, then top with turkey and a few spoonfuls of gravy. Transfer sandwiches to plates and serve immediately.