Start by washing and chopping the broccoli into small florets.

In a large pot, heat a little oil over medium heat. Add the chopped onion and sauté until it becomes translucent, about 5 minutes.

Stir in the minced garlic and sauté for another minute.

Add the broccoli florets to the pot, along with the vegetable broth. Bring this mixture to a boil, then reduce the heat and let it simmer for about 10 minutes, until the broccoli is tender.

Using an immersion blender, puree the soup until it reaches your desired consistency.

Return the soup to the pot and stir in the heavy cream.

Gradually add the shredded cheddar cheese, stirring until it has melted completely.

Finally, season with salt, pepper, and nutmeg, if using.