In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté for about 3-4 minutes until translucent.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the diced carrots and fresh broccoli florets to the pot, cooking for another 5 minutes, stirring occasionally.
Pour in the vegetable broth and bring the mixture to a boil. Once boiling, reduce heat and simmer for about 15 minutes until the broccoli and carrots are tender.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup in batches to a standard blender and blend until smooth.
Return the soup to low heat and stir in the heavy cream and shredded cheddar cheese, mixing until the cheese is completely melted and integrated.
Add the Dijon mustard, salt, and pepper to taste, stirring well.
Serve hot, garnished with croutons and fresh herbs if desired.
Notes
For a lighter version, substitute heavy cream with coconut cream.