Heat oil in a soup pot over medium heat. Add celery, carrot, onion, jalapeno pepper, and garlic. Cook and stir until onion is softened, about 5 minutes. Add potatoes and enough water to cover. Add bouillon and bring to a boil, about 5 minutes. Cook until potatoes and carrots are soft, about 40 minutes.
Remove soup from heat and use a hand blender to puree until creamy. Add asparagus and bring soup to a boil. Cook until asparagus is tender but not soft, about 5 minutes more. Add salt and pepper.
