In a large skillet over medium, heat olive oil, and add onion once oil is hot. Cook onion until tender. Stir in soup, sour cream, peas and carrots, broccoli, rosemary, and garlic. Mix well and remove from heat.
Place mixture in a large casserole dish that’s been sprayed with non-stick cooking spray. Sprinkle Parmesan cheese over the top, and bake, covered, 20 minutes. Remove the cover, and continue cooking 10 minutes or until heated through and bubbling.