In a medium bowl, mix the turkey, shallot, parsley, paprika and poultry seasoning; season with salt and pepper. Score the meat mixture into 4 sections and form thin patties. In a large nonstick skillet, heat the EVOO, 1 turn of the pan, over medium-high heat and cook the patties for 6 minutes on each side. Transfer to a plate, wipe the pan clean and set aside.
Combine the horseradish mustard and relish in a small bowl. Butter 1 side of each slice of bread. Make the sandwiches with the buttered sides facing out. Spread some mustard mixture on half the bread slices and top with a slice of cheese, a few forkfuls of sauerkraut, a patty and another slice of cheese; set the top slices of bread into place. Heat the skillet to medium-low and grill the sandwiches, turning once, until crisp and golden and the cheese melts, about 5 minutes total.