Preheat the broiler. Season the turkey with the poultry seasoning, salt and pepper, then form into 4 thin patties. Broil, turning once, until brown on both sides and cooked through, about 6 minutes.
For each sandwich, layer a bread slice, a cheese slice, a turkey patty, another cheese slice and another bread slice. In a large skillet, heat a little butter and grill the sammies until the cheese melts and the bread is browned and crispy.