1Melt butter in a large pot over medium heat. Add the diced onion and cook, stirring occasionally, for 10–12 minutes until deeply golden and sweet.
2Stir in the minced garlic and cook for 1 minute until fragrant.
3Add the broccoli florets and stems, then pour in the vegetable broth. Bring to a simmer and cook for 12–15 minutes until the broccoli is very tender.
4Using an immersion blender, puree the soup until smooth. (Alternatively, carefully transfer half the soup to a blender, puree, and return to the pot.)
5Reduce heat to low. Stir in the heavy cream and then add the shredded cheddar cheese in handfuls, stirring until fully melted and smooth.
6Season with salt, black pepper, and a pinch of nutmeg. Taste and adjust seasoning as needed. Serve hot.