In a large pot, heat 1 tablespoon of the olive oil over medium-high heat; add the sausage and cook, stirring, until golden, about 5 minutes, just to crisp the sausage and render some of its flavor into the oil. Using a slotted spoon, transfer the sausage to a bowl.
Add the remaining olive oil and the onion to the pot and cook until starting to become golden, about 5 minutes. Then stir in the garlic and cook about 1 minute more.
Stir in the potatoes and chicken broth and bring to a simmer; season with salt and pepper. Cook until the potatoes are almost tender, 8 to 10 minutes. Stir in the asparagus and the chopped herbs, and cook until tender, about 5 minutes (less if it's been roasted). Remove from the heat.
Scoop out ¼ cup asparagus tips and set aside for garnish. Use an immersion blender to puree the soup.
Whisk in the coconut milk, except for what you’ve reserved for garnish. Taste and season with salt and pepper. Stir in three-fourths of the sausage pieces and allow to warm in the soup for a couple of minutes.
Ladle the soup into bowls, swirl with a tablespoonful per bowl of coconut milk, sprinkle the remaining sausage and asparagus pieces on top and serve.