In a large pot, heat olive oil over medium heat. Sauté chopped onion and minced garlic until soft and fragrant (about 5 minutes).

Add broccoli florets, salt, and pepper; sauté for another 5 minutes until bright green and tender-crisp.

Pour in stock, ensuring vegetables are submerged. Bring to a gentle boil; then reduce heat and simmer for about 10 minutes until broccoli softens.

Blend the mixture using an immersion blender until smooth. For a chunkier texture, blend only half.

Return soup to low heat; stir in heavy cream and shredded cheddar cheese until melted.

Serve hot, garnished with extra cheese or crispy bacon bits if desired.