Wash asparagus thoroughly. Snap off the woody ends (they will naturally break at the right point). Cut the tender spears into 1-inch pieces. Reserve a few small tips for garnish if desired.

In a large pot or Dutch oven, heat olive oil and butter over medium heat. Add the chopped yellow onion and cook, stirring occasionally, until softened and translucent, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Add the cut asparagus pieces (excluding reserved tips) to the pot. Sauté for 5-7 minutes, stirring frequently, until the asparagus is bright green and slightly tender-crisp. This step is crucial for developing a rich, "sautéed asparagus" flavor.

Pour in the vegetable broth. Bring the mixture to a simmer, then reduce heat to low, cover, and cook for 10-12 minutes, or until the asparagus is very tender.

Carefully remove the pot from the heat. Using an immersion blender, blend the soup directly in the pot until completely smooth and creamy. If you don't have an immersion blender, transfer the soup in batches to a regular blender (be careful with hot liquids, vent the lid, and blend in small quantities). Return blended soup to the pot.

Stir in the heavy cream. Reheat gently over low heat, do not boil. Season generously with salt and freshly ground black pepper to taste. If using, quickly blanch reserved asparagus tips in boiling water for 1-2 minutes until tender-crisp, then add to soup bowls as garnish.

Ladle the hot soup into bowls. Garnish with fresh chopped parsley, a drizzle of olive oil, or a sprinkle of Parmesan cheese if desired. A squeeze of lemon juice at the end can brighten the flavors.