Start a pot of water to boil for the eggs. While waiting, trim the asparagus by snapping off the woody ends (they'll naturally break at the tender point) and cut the spears into 1-inch pieces, separating the tender tips from the thicker stem pieces. Once the water boils, add eggs and cook for 10-12 minutes until hard-boiled. While eggs cook, dice the ham into 1/2-inch cubes and finely chop the parsley. When eggs are done, cool them in ice water, then peel and finely chop them into 1/4-inch pieces.
Melt the butter in a large pot over medium heat, then add the flour and stir constantly for about 2 minutes to cook out the raw flour taste—this creates the foundation for your sauce. Meanwhile, bring the vegetable stock to a boil in another pot and add the asparagus tips with the sugar. Simmer for 10 minutes until the tips are tender-crisp, then remove them with a slotted spoon and set aside. I like to save the asparagus tips separate because they stay vibrant and add a beautiful texture contrast in the finished soup.
To the same pot of stock with the cooked tips removed, add the remaining asparagus stem pieces and simmer for 20 minutes until very tender. Carefully blend the cooked asparagus and stock together until completely smooth using an immersion blender or regular blender in batches—this creates the silky texture that defines this soup. Slowly whisk the smooth asparagus purée into the flour-butter roux from Step 2, stirring constantly to avoid lumps and create a cohesive sauce.
Heat the soup over medium heat for 5 minutes, stirring occasionally, to fully incorporate all components and develop the flavors. Reduce heat to low and stir in the heavy cream, then add the salt, white pepper, and nutmeg. Taste and adjust seasonings as needed—I find the nutmeg is key here as it brings out the earthy asparagus flavor without being noticeable.
Ladle the hot soup into bowls and top each serving with the reserved asparagus tips, diced ham, chopped hard-boiled eggs, and a sprinkle of fresh parsley. The garnishes add color, texture, and little pockets of flavor that make each spoonful interesting.