Bring a large pot of generously salted water to a boil. Cook tortellini according to package directions until just tender, about 4 minutes. Drain and rinse under cold water until cool.

In a large bowl, whisk the olive oil, vinegar, mustard, garlic, oregano, salt, and pepper until emulsified.

Halve the tomatoes, dice the cucumber and bell pepper, and thinly slice the onion. If using, dice the salami. Toss the sliced onion with a small spoonful of the dressing to mellow it.

Add the cooled tortellini, all vegetables, olives, salami, and basil into the dressing bowl. Fold gently until everything is coated.

Toss once more, top with extra basil, and serve at room temperature or chilled.