In a pot, heat avocado oil over medium heat. Add onion and garlic and cook until soft and beginning to brown, approximately 6 minutes. Add cauliflower, fennel and broth. Bring to a boil, then lower heat to low, cover and simmer for 10 minutes until vegetables are cooked and soft. Add sea salt and pepper, to taste.

Using an immersion blender, blend soup until smooth. Alternatively, carefully put hot soup into a blender and blend until smooth.