In a small bowl, stir together red onion, thyme, mayonnaise, and mustard. Spread some of this mixture onto one side of each slice of bread. Spread butter onto the other side of each slice.

Heat a large skillet over medium heat. Place bread slices, butter-side down, into the skillet. Layer each slice with 1/4 of the sliced turkey, two slices of tomato, and two slices of Swiss cheese. Place remaining bread, butter-side up, on top. Cook until bread is golden brown, about 10 minutes, flipping halfway through.