Heat 1 tablespoon oil in a large saucepan over medium heat. Add shallot and cook, stirring, until softened, 2 to 3 minutes. Add broth, asparagus, potato, horseradish and salt; bring to a boil. Reduce heat and simmer until the vegetables are tender, about 15 minutes. Puree with an immersion blender or in a regular blender. (Use caution when pureeing hot liquids.)
Meanwhile, heat the remaining 1½ tablespoons oil in a large skillet over medium-high heat. Reduce heat to medium, add bread cubes and cook, stirring, until browned and crispy, 3 to 5 minutes.
Serve the soup topped with the croutons and scallions, if desired.
