Preheat your oven to 425°F (220°C). Toss the broccoli florets with olive oil, salt, and pepper on a baking sheet until evenly coated. Roast for about 20 minutes until tender and crispy.

In a large pot over medium heat, melt some butter. Add the diced yellow onion and sauté until translucent, about 5 minutes.

Stir in the minced garlic and cook for another minute.

Add the roasted broccoli and low-sodium vegetable broth to the pot. Let this mixture simmer for about 10 minutes.

Using an immersion blender, blend the soup until smooth. Reserve some broccoli bits for texture if desired.

Stir in the shredded cheddar cheese until melted, then add the heavy cream.

Serve hot in bowls, garnished with extra cheese or croutons if desired.