Cook tortellini according to package directions; drain.
Whisk together the oil and vinegar until emulsified. Stir in the garlic and season with salt and pepper. Toss the dressing with warm tortellini.
Stir in parsley, green onions, red pepper, basil and artichokes hearts.
Blanch broccoli in boiling water until bright green (about 1 minute); drain. Rinse with cold water; drain.
Refrigerate salad and broccoli separately, covered, several hours or overnight.
To serve, toss Parmesan cheese and broccoli with salad. Spoon into serving bowl. Garnish with cherry tomatoes.