Heat oil in a large pot over medium heat. Add onion and sauté until soft and translucent (about 5-10 minutes). Add garlic and cook for about 1 more minute, stirring.
Add cauliflower, broth, and pumpkin. Bring to a boil; cover, and simmer for about 15-20 minutes or until cauliflower is tender.
Stir in Parmesan and coconut; give the soup a taste to check for seasoning. Add salt or pepper, if desired.
Remove from heat and use an immersion blender to puree the soup until smooth. If you don’t have an immersion blender, just transfer the soup to a large blender and puree until smooth. Be careful with the hot soup!