Drain the mozzarella pearls, artichoke hearts and olives, and pat the mozzarella dry. Quarter the artichoke hearts and cut the cucumber into 12 thin rounds.
Fold each salami slice in half twice so it sits flat on the skewer.
Thread 12 skewers, adding to each: 2 cherry tomatoes, 1 basil leaf, 2 mozzarella pearls, 1 artichoke quarter, 1 cucumber round, 1 olive and 1 folded salami slice.
Arrange the skewers on a platter and refrigerate for up to 4 hours.
Whisk the olive oil with the black pepper, drizzle over the skewers, then drizzle with balsamic glaze just before serving.