In a large pot, heat the olive oil over medium heat. Add the chopped 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 to the pot and pour in the vegetable broth. Bring to a boil, then reduce the heat to a simmer. Cover and cook for about 10-15 minutes until the broccoli is tender.
Use an immersion blender to puree the soup until smooth. (If you don’t have an immersion blender, carefully transfer the soup to a countertop blender in batches.)
Return the pureed soup to the pot and stir in the milk, softened cream cheese, and Dijon mustard. Mix well until the cream cheese is fully melted and incorporated.
Gradually add the shredded cheddar cheese, stirring continuously until melted and creamy.
Season with salt and pepper to taste. If the soup is too thick, adjust the consistency with more milk or broth.
Serve hot, garnished with croutons and fresh parsley if desired.
Notes
For a thicker soup, add less broth. Garnish with croutons and parsley for extra flavor.