Break off or cut the thick, woody ends of the asparagus. Then, cut asparagus spears into thirds.
Heat olive oil on medium-high heat. Once shimmery/ hot, add the asparagus and cook for 3-4 minutes, stirring occasionally.
Add the garlic and cook another minute, stirring occasionally.
Add the broth, enough to just cover all of the asparagus. Once it is starting to boil, lower the head to medium-low and cover. Let cook for 10 minutes, or until asparagus is very tender.
Either add to a blender or use a hand-held emulsifier and blend until pureed.
Add back to the stove and add the coconut milk. Cook for another 5 minutes, or longer if you want it thicker, on medium heat, stirring occasionally.
Season with pepper and any extra salt you may need. Then, it is ready to serve!
