Begin by heating the olive oil in a small skillet over medium heat, then add the minced garlic and cook until fragrant and lightly golden, about 1 minute.
Transfer the sautéed garlic and oil into the slow cooker, then add the chopped broccoli and vegetable broth.
Cover and cook on low for about 6 hours, until the broccoli is tender and the flavors meld together.
Once cooked, blend the soup until smooth using an immersion blender directly in the slow cooker or transfer to a blender in batches, being careful of the hot liquid.
Add the shredded cheese and heavy cream to the blended soup, stirring well until melted and fully incorporated to give a creamy consistency.
Season with salt and pepper to taste, then give it a final stir to evenly distribute the seasonings.
Taste the soup and adjust seasoning if needed, then ladle into bowls to serve hot, garnished with extra cheese or a drizzle of cream if desired.
