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

Stir in the minced garlic and cook for an additional minute until fragrant.

Add the broccoli florets and potato to the pot, stirring to combine. Cook for about 3-4 minutes.

Pour in the vegetable broth and bring the mixture to a boil. Reduce the heat and let it simmer for 15-20 minutes, or until the broccoli and potato are tender.

Using an immersion blender, carefully puree the soup until smooth. If you don't have an immersion blender, transfer the soup in batches to a regular blender.

Once blended, return the soup to the pot and stir in the heavy cream, salt, black pepper, and nutmeg.

Gradually add the shredded cheddar cheese, stirring until melted and well combined.

Taste and adjust seasoning if necessary. Serve hot, garnished with croutons and extra cheddar if desired.