In a large pot or Dutch oven, melt the butter over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for another minute until fragrant.
Add the broccoli florets, shredded carrots, and dried thyme. Stir everything together for a couple of minutes.
Pour in the vegetable broth, bring the mixture to a boil, then reduce the heat and let it simmer for about 15 minutes or until the broccoli is tender.
Using an immersion blender, blend the soup until smooth. Alternatively, you can transfer the soup in batches to a countertop blender, then return it to the pot.
Stir in the heavy cream and heat gently. Add the grated cheddar cheese gradually, stirring continuously until melted and creamy.
If using, mix in the Dijon mustard for an extra depth of flavor. Season with salt and pepper to taste.
Serve the soup hot, garnished with chopped chives or parsley for a fresh touch.
Notes
Serve in wide bowls topped with extra cheese and fresh herbs. Croutons can be added for crunch.