Instructions:
- Place eggs in a saucepan, cover with cold water plus one inch, and bring to a rolling boil. Once boiling, immediately cover, remove from heat, and let stand for exactly 10 minutes.
- While eggs stand, prepare a large bowl filled with ice and cold water (ice bath). Immediately transfer the hot eggs to the ice bath and chill for at least 15 minutes until completely cooled.
- Carefully peel the cooled eggs. Slice them lengthwise and gently scoop the yolks into a medium mixing bowl. Arrange the egg white halves on a serving platter.
- Mash the egg yolks thoroughly with a fork until smooth. Whisk in the mayonnaise, Dijon mustard, salt, and pepper until the mixture is creamy.
- Gently fold in the diced mozzarella, prepared tomatoes, and most of the chopped basil into the yolk mixture. Avoid over-mixing to keep texture intact.
- Spoon or pipe the Caprese filling mixture evenly back into the reserved egg white halves.
- Refrigerate the filled eggs for at least 30 minutes to allow the filling to firm up.
- Just before serving, drizzle generously with balsamic glaze and garnish each half with a small fresh basil leaf or sprig.