Mix softened butter and mayonnaise in a small bowl. This creates the spread for the outside of the bread.

Spread the butter mixture on one side of each slice of sourdough. Sprinkle generously with cracked black pepper and garlic powder.

Flip bread over. Spread a thin layer of Dijon mustard on the inside (unbuttered side) of one slice.

Layer half the cheese on the mustard side, followed by the folded ham slices, and topped with the remaining cheese. Close the sandwich with the second slice of bread, buttered side out.

Place sandwich in a skillet over medium-low heat. Cook for 3-5 minutes per side, covering the pan with a lid for the first 2 minutes to help steam the cheese.

Once both sides are deep golden brown and cheese is fully melted, remove from heat.

Let rest for 1 minute before slicing in half to serve.