In a large pot, melt the butter over medium heat. Add the chopped onion and garlic, and sauté for about 3-4 minutes, until soft and fragrant.
Add the broccoli florets to the pot and pour in the broth. Bring the mixture to a boil, then reduce heat and let it simmer for 10 minutes or until the broccoli is tender.
Using an immersion blender or a regular blender, puree the soup until it reaches your desired consistency. If you like it chunkier, leave some broccoli pieces intact.
Return the soup to the pot (if using a regular blender) and stir in the heavy cream, cheddar cheese, salt, pepper, and nutmeg. Simmer for another 5 minutes, stirring occasionally, until the cheese is melted and the soup is smooth and creamy.
Taste and adjust seasoning if necessary. Serve hot, garnished with extra shredded cheese or a drizzle of olive oil.
Enjoy this creamy and hearty keto broccoli soup as a warm, filling meal or side dish that fits perfectly into your keto lifestyle!