Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the tortellini and return to a boil. Cook until the pasta floats to the top, 1 to 2 minutes; drain.
Heat sesame oil in a large skillet or wok over medium-high heat; cook and stir meatballs, pineapple chunks, and hoisin sauce until meatballs are heated through, 7 to 10 minutes. Transfer meatball mixture to a bowl and set aside.
Heat olive oil in the same skillet until oil begins to shimmer. Add broccoli, cauliflower, carrots, green bell pepper, red bell pepper, zucchini, celery, and green onions. Season with salt and pepper. Cook and stir until vegetables are just tender, about 5 minutes. Stir tortellini and meatball mixture into vegetable mixture until hot. Sprinkle with parsley and Parmesan cheese to serve.