Wash and chop the fresh broccoli into bite-sized florets, dice the onion, peel and slice the carrots, and mince the garlic.

In a large pot, heat a tablespoon of olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent.

Stir in the minced garlic and sliced carrots, cooking for an additional 3-4 minutes until the carrots are somewhat softened.

Stir in the chopped broccoli and pour in 4 cups of vegetable broth. Increase heat to bring to a boil, reduce to a simmer.

Let it cook for about 10-12 minutes, or until the broccoli is vibrant green and tender.

Use an immersion blender to puree the soup until smooth and creamy, about 1-2 minutes.

Stir in 2 cups of shredded cheddar cheese until fully melted, then whisk in 1 cup of milk.

Mix 2 tablespoons of cornstarch with a little water to create a slurry and add it to the soup, simmer for another 2-3 minutes.

Season with salt and pepper to taste, serve hot with extra cheese or fresh herbs.