Heat the olive oil in a large pot over medium heat. Add the chopped onions and sauté until they are translucent, about 5 minutes.
Add the minced garlic to the pot and cook for an additional minute until fragrant, stirring frequently to avoid burning.
Add the broccoli florets to the pot, followed by the vegetable broth. Bring the mixture to a boil, then reduce the heat to a simmer. Cover and let it cook for about 15 minutes, or until the broccoli is tender.
Once the broccoli is tender, remove the pot from heat and let it cool slightly. Carefully transfer the mixture to a blender in batches, or use an immersion blender directly in the pot. Blend until smooth.
Return the blended soup to the pot over low heat. Stir in the heavy cream and season with salt and pepper to taste. Heat gently until warmed through but do not boil.
Serve the soup hot. Garnish with croutons and shredded cheese if desired.
For a vegan version, substitute heavy cream with coconut milk or a plant-based cream alternative.
For added nutrition, consider blending in a handful of spinach or kale when pureeing the soup.