1. In a 5- to 6-quart pan over medium heat, stir onions often in olive oil until limp, about 10 minutes.
2. Stir in carrots and potatoes. Add chicken broth and bring to a boil over high heat. Cover pan, reduce heat, and simmer, stirring occasionally, until potatoes and carrots are tender when pierced, about 20 minutes.
3. Working in small batches, transfer soup to a blender or food processor and whirl until smooth. Pour into a large bowl.
4. Return the soup to the pan and stir often over medium heat until hot. Add salt to taste. Ladle into bowls and top each serving with a dollop of roasted tomatillo relish.