In a large soup pot, heat oil over medium-low heat.
Add onions and garlic to pot and saute 1-2 minutes or until fragrant.
Add carrots, broccoli, and broth to pot and simmer 10-20 minutes, or until veggies are tender.
Add half n half to pot. Using an immersion blender, puree for a couple minutes until desired consistency.
Lastly, add cheese and stir until melted. Enjoy!