Heat the olive oil in a large pot over medium heat. Add the chopped onion and sauté for about 3-4 minutes, until translucent.
Add the minced garlic and cook for an additional minute until fragrant.
Stir in the diced carrots, celery, and bell pepper. Cook for about 5 minutes, stirring occasionally, until the vegetables are slightly softened.
Add the diced zucchini, vegetable broth, dried thyme, salt, and black pepper. Bring the mixture to a boil.
Once boiling, reduce the heat and simmer for about 10 minutes.
Add the broccoli florets and frozen corn, cooking for another 5-7 minutes until the vegetables are tender.
If desired, use an immersion blender to puree a portion of the soup for a creamier texture.
Stir in the shredded cheddar cheese until melted and smooth. If you want a richer soup, add the heavy cream at this point and mix well.
Serve hot, garnished with additional cheese if desired.