Bring a large pot of salted water to a boil. Cook the refrigerated tortellini according to the package directions, usually about 3–7 minutes, until just tender; the full cooking process generally takes about 8–12 minutes when boiling and draining are included.

Drain the tortellini well and rinse briefly under cold water to stop the cooking. Toss it with a small amount of dressing or olive oil, then cool completely so the pasta does not stick.

Whisk the olive oil, lemon juice, lemon zest, Dijon mustard, honey, garlic, kosher salt, and black pepper in a small bowl. You can also place everything in a jar with a tight-fitting lid and shake until combined.

Add the cooled tortellini, chicken, cherry tomatoes, cucumber, red onion, olives, parsley, basil, and spinach, if using, to a large bowl.

Pour the dressing over the salad and toss gently until the ingredients are evenly coated. Add Parmesan, if desired, and refrigerate for 30 minutes before serving.

Toss the salad again immediately before serving. If it needs refreshing after chilling, stir in the reserved 1–2 tablespoons of dressing.