Make the balsamic glaze: Add balsamic vinegar and honey to a small saucepan. Simmer over medium heat until reduced by half, stirring occasionally. Lower the heat if needed to avoid boiling. Set aside to cool.

Prepare the basil pesto according to your recipe instructions.

Butter one side of each slice of bread. Flip and spread a generous layer of pesto on the other side.

On the pesto side, layer arugula, basil leaves, sliced tomatoes, and fresh mozzarella. Season lightly with salt and pepper and drizzle with balsamic glaze.

Top with the second slice of bread, pesto side facing inward.

Grill on a panini press or grill pan until golden and crisp, and the cheese is melted. Serve the Balsamic Glazed Caprese Panini immediately.