Spread one side of each slice of bread with butter. Spread each unbuttered side with about 2 tablespoons bacon jam. Layer sandwich with 1-1/2 slices swiss cheese, followed by half of the peach slices, half of the baby arugula leaves, and another 1-1/2 slices of cheese, and a second piece of the prepared bread. Repeat with remaining ingredients to assemble second sandwich.
Cook sandwiches in a nonstick pan or griddle over medium-low heat until bread is golden and cheese is melted, pressing the sandwich with a spatula or grill press as it cooks. Serve immediately.
Homemade Bacon Peach Jam is a delicious addition to these grilled cheese sandwiches; as a timesaver, they can also be made with your favorite commercially-prepared bacon jam.