Cut ½ cup asparagus tips, 1 ½-inch from the top, for garnish. Set aside. Cut remaining asparagus into 1-inch pieces.
Heat oil and butter in a large pot over medium heat and add the onions, ½ teaspoon salt, and a pinch of black pepper. Sauté for about 5 minutes, until onions are translucent and soft. Stir in minced garlic and thyme and cook for another minute.
Add potatoes and 1 cup stock, cover, and simmer for about 10 minutes, or until potatoes are fork-tender.
Add asparagus, 4 cups stock, and ½ teaspoon salt and bring to a boil. Allow to simmer uncovered on low heat for about 15 to 20 minutes, or until asparagus is tender.
While soup is simmering, prepare the asparagus tips. Bring water to a boil in a small saucepan. Lightly salt and drop in asparagus. Blanch for about 1 ½ minutes, or until bright green and just tender. Remove with slotted spoon. Set aside.
After asparagus has cooked, add parsley and puree with immersion blender or standup blender. Stir in cream, if using, vermouth, and lemon juice. Taste and adjust seasoning as needed.
Serve soup hot or at room temperature. Top each bowl with a wedge of Humboldt Fog and an asparagus tip to garnish.