Bring a large pot of salted water to a boil. Cook the tri-color rotini according to the package directions until al dente, usually 9–12 minutes.

Drain the pasta and rinse it briefly under cold water to stop the cooking and cool it. Drain thoroughly so excess water does not thin the dressing.

While the pasta cooks, prepare the vegetables and cheese. Halve the tomatoes, dice the cucumber and bell peppers, cut the broccoli into small florets, slice or dice the red onion, slice the olives, and chop the parsley if using.

Whisk together the olive oil, red-wine vinegar, lemon juice, Dijon mustard, honey or sugar, garlic, Italian seasoning, kosher salt, and black pepper. You can also shake everything in a jar with a tight-fitting lid.

Add the cooled pasta, tomatoes, cucumber, bell peppers, broccoli, onion, olives, and cheese to a large bowl. Pour in about three-quarters of the dressing and toss gently until the ingredients are evenly coated.

Refrigerate the salad for at least 30 minutes before serving. Add the remaining dressing if the pasta has absorbed too much, then garnish with parsley.