In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté for about 3-4 minutes until translucent.
Add the minced garlic and diced carrots to the pot. Sauté for another 2-3 minutes until the carrots are slightly softened.
Stir in the broccoli florets, vegetable broth, and dried thyme. Bring to a boil, then reduce heat and let simmer for about 15 minutes, or until the broccoli is tender.
Once the vegetables are soft, use an immersion blender to blend the soup until it reaches your desired level of creaminess. If you don’t have an immersion blender, carefully transfer the soup in batches to a regular blender and purée.
After blending, return the soup to low heat. Stir in the heavy cream and mix well. Slowly add the cheddar cheese, a little at a time, stirring continuously until melted and creamy.
Season with salt and pepper to taste. If the soup is too thick, you can add a bit more vegetable broth to reach your preferred consistency.
Serve hot, garnishing with croutons and a sprinkle of fresh parsley if desired.
Notes
Add more vegetable broth if the soup is too thick.