Slice off the pretty tips of the asparagus about 1 - 1 1/2 inches long and reserve. Trim the woody ends of the asparagus and discard. Cut the remaining spears into 1" pieces and set aside.
In a large saucepan, heat the olive oil over medium heat and add the shallots and 1/4 teaspoon salt. Cook until the shallots soften and become translucent - do not brown the shallots.
Add the asparagus, potato and sun chokes to the shallots. Add vegetable broth, cover and bring just to a boil. Turn down the heat to simmer and cook for 20 minutes until vegetables are tender.
Meanwhile, in a small saucepan, bring a cup of water to a boil. Prepare an ice bath by adding 1 cup of ice and 1 cup water into a bowl and set aside.
Add the asparagus tips to the boiling water and cook for 1-2 minutes until just tender. Use a slotted spoon or spider to transfer the asparagus tips from the boiling water to the ice bath to shock them and stop the cooking. Set aside until ready to serve.
When the potatoes, asparagus and sun chokes are tender, transfer the vegetables and broth to a blender and puree until smooth. Season with the kosher salt and pepper.
To serve, ladle the soup into bowls and swirl a teaspoon of olive oil over each bowl. Divide the asparagus tips among the bowls and float them in the soup. Top with a pinch of microgreens if desired.