Spread butter on one side of each bread slice. Spread mustard on remaining side of each bread slice.
Split sausages lengthwise without cutting all the way through.
Heat a griddle over medium-high heat and lightly spray with cooking spray. Place sausages on griddle, cut side down, and cook until browned, about 4 minutes. Turn sausages and cook until browned, 4 minutes more. Remove from skillet.
Reduce heat to medium. Divide pastrami into 4 stacks. Place pastrami stacks on griddle and cook until heated through and lightly browned, 2 minutes. Turn pastrami stacks and top each with 1 cheese slice; cook until melted, about 2 minutes.
Arrange 1 pastrami stack on mustard side of each of 4 bread slices. Top each with 1 cheese slice, 1 sausage, and remaining bread slices, mustard side down.
Place assembled sandwiches on griddle and toast, turning halfway through, until golden brown, 1 to 2 minutes per side.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/sailor-sandwiches/