Add coconut oil to a large heavy-bottomed pot over medium heat. Add onions and garlic and sauté until onions are translucent and become fragrant.
Add chopped asparagus, stirring until well combined. Pour chicken broth over asparagus and onions. Add salt and pepper, tasting to check for seasonings.
Cover pot with lid and low boil until asparagus is tender, 15 to 20 minutes. Take soup off of burner and allow to cool slightly.
Add soup to a blender and blend until smooth. Pour soup back into the pot and heat on medium until heated through.
Notes
Don't have an upright blender? You can use an immersion blender for this recipe, but make sure it is blending completely or the soup will not turn out smooth.