Start by peeling the asparagus with a vegetable peeler. Don't be afraid to peel off a lot; you'll appreciate it later.

Break each asparagus with your hands and set aside the tougher lower parts and any very short tips.

Dice the onion and put it in a pot with oil. Season with salt and pepper and let it cook.

When it starts to turn golden, add the lower asparagus stalks, adjust the salt, stir a couple of times, and let them cook for a few minutes.

Peel the potato, cut it into chunks, and add it. Stir a couple of times, adjust the salt, and let it cook for about five more minutes, stirring occasionally.

Cover with water, add the short tips, and let it simmer until the potatoes are soft.

Cook the remaining asparagus tips in a separate pot with salt and a tablespoon of sugar to remove the bitterness. Let them cook for about 10 minutes.

Once the potatoes are soft, remove the pot from the heat and blend the mixture. Add the cream, adjust the salt, and blend until smooth.

If desired, strain the soup to remove any asparagus fibers.

Once the tips are cooked, place them in ice water to stop the cooking process and cool them down.

Pour the soup into serving bowls and add some asparagus tips as a garnish. Drizzle with a few drops of olive oil. Serve it cold or at room temperature, as you prefer. You can also accompany it with some croutons.