It's best to use very thinly sliced ham, not thick ham steaks. Ask your deli to slice it, or look for a packet of center- and end-cut slices, which tend to be smaller.
Spread each of 4 bread slices with 1 tsp. mustard, and sprinkle with desired amount of freshly ground pepper. Layer with cheese, ham, peaches, and, if desired, honey. Top with remaining bread slices, and press together gently. Brush sandwiches with olive oil.
Cook sandwiches, in batches, in a preheated panini press 3 to 4 minutes or until golden brown and cheese is melted. (Or use a preheated nonstick grill pan, and cook sandwiches over medium heat 3 to 4 minutes on each side.) Serve immediately.
*Any firm white bread may be substituted.