Bring a small pot of lightly salted water to a boil. Cook tortellini in the boiling water until pasta floats to the top, 1 to 2 minutes; drain. Thread 1 tortellini, 1 salami slice, 1 sprig parsley, 1 artichoke heart quarter, 1 tomato half, 1 mozzarella cheese cube, and 1 olive half, respectively, onto a toothpick. Repeat threading with remaining toothpicks.