Preheat an electric sandwich press and grill or grill pan to medium high. These sandwiches can also be made in a regular skillet if you don't have a sandwich press.
Place the split bratwurst on the grill or grill pan and cook until marked and heated through. Keep pressing them down while they cook so they don't curl up.
While the bratwurst are cooking, combine the sauerkraut and relish in a bowl. Place 4 slices of the onion rye on a cutting board, spread them with a little mustard and top with a slice of the havarti. Top the cheese with a grilled bratwurst -- cutting the bratwurst to fit your bread -- some of the relish/sauerkraut mixture, then another slice of the havarti.