Preheat the oven to 425 degrees Fahrenheit. Lightly spray a large baking sheet with cooking spray; set aside.
In a small bowl, whisk together the olive oil, balsamic vinegar, Italian seasoning, paprika, salt, and pepper. In a large mixing bowl, combine potatoes, zucchini, bell pepper, red onion, mushrooms, and garlic.
Drizzle the oil mixture over the vegetables and toss to coat, then spread them in an even layer on the baking sheet. Gently toss the vine tomatoes in the remaining oil, then nestle them in the vegetables. Top with the rosemary sprigs.
Roast for 30 to 35 minutes, or until tender and just beginning to char, being sure to stir halfway through the cooking time.
Serve garnished with fresh parsley, if desired.