Preheat your oven to 200°C (400°F). Toss the broccoli florets with olive oil, salt, and pepper, then spread them out on a baking sheet. Roast for 20-25 minutes until edges are slightly charred and fragrant, which will develop a smoky sweetness in the broccoli.
While the broccoli roasts, melt the butter in a large heavy-bottomed pot over medium heat. Add the chopped onion and cook, stirring occasionally, until translucent and soft, about 5 minutes. The aroma should be warm and slightly sweet.
Add the minced garlic to the pot and cook for another minute, until fragrant. Be careful not to burn the garlic, as it can turn bitter.
Pour in the vegetable broth and bring it to a gentle simmer. Once simmering, add the roasted broccoli to the pot and cook for about 10 minutes, allowing the flavors to meld and the broccoli to become tender.
Use an immersion blender directly in the pot, or carefully transfer the mixture in batches to a blender. Puree until the soup is smooth and velvety. This step creates the creamy base that makes the soup feel luxurious.
Stir in the shredded cheddar cheese gradually over low heat, stirring constantly until melted and glossy. Then, add the heavy cream and mix well. Taste and season with salt and pepper as needed.
Allow the soup to simmer gently for another 5 minutes, stirring occasionally. The mixture should thicken slightly, with a rich, cheesy aroma filling your kitchen.
Taste the soup and adjust seasoning if necessary. Ladle into bowls, garnish with extra cheese or herbs if desired, and serve hot. The soup should be thick, smooth, and inviting, with a smoky sweetness from the roasted broccoli.
