Heat the olive oil in a large pot over medium heat. Add the diced onion and sauté for about 5 minutes, or until translucent.
Add the minced garlic and cook for an additional minute until fragrant.
Stir in the broccoli florets and diced potato, cooking for another 3 minutes to combine the flavors.
Pour in the vegetable broth and bring the mixture to a boil. Reduce the heat and let it simmer for about 15-20 minutes, or until the broccoli and potato are tender.
Using an immersion blender, blend the soup until smooth, or transfer carefully to a blender in batches.
Return the blended soup to the pot and stir in the heavy cream, shredded cheddar cheese, and Dijon mustard. Mix well until the cheese is fully melted and incorporated.
Season with salt, pepper, and red pepper flakes (if using) to taste. Let it simmer gently for another 5 minutes.
Serve hot, garnished with additional cheddar cheese or a sprinkle of red pepper flakes if desired.
Notes
Garnish with additional cheddar cheese or red pepper flakes if desired.