Spread butter on one side of each piece of sourdough bread and lay the slices butter-side down on a plate. For each sandwich, spread the un-buttered side of only one slice of bread with Dijon.

Cover just the mustard-spread slices of bread with a generous amount of shredded cheese, then follow with a layer of sliced peaches. Top each sandwich with another slice of bread, butter-side up.

Place the sandwich in a non-stick pan over medium heat. Cover with the lid and let them cook for 3 to 4 minutes, or until golden.

Lower the heat to medium and very carefully flip the sandwiches, making sure they do not fall apart while flipping. cook for another 2 or 3 minutes, until the bread is golden brown and the cheese is melted. The second side will cook faster than the first, so keep an eye on it. Slice each sandwich in half and serve immediately.