In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent.
Add the minced garlic and sauté for an additional minute until fragrant.
Stir in the broccoli florets and vegetable broth. Bring to a boil, then reduce heat and let it simmer for about 10-15 minutes, or until the broccoli is tender.
Using an immersion blender, carefully blend the soup until smooth. If you do not have an immersion blender, you can blend in batches using a traditional blender—just be cautious with the hot liquid.
Return the blended soup to the pot over low heat. Stir in the heavy cream, cheddar cheese, mustard powder, black pepper, and salt. Mix until the cheese has melted and the soup is creamy.
Adjust seasoning to taste, adding more salt or pepper if needed.
Serve hot, garnished with croutons if desired.
Notes
Adjust seasoning to taste and serve with croutons for added texture.