In a 5- to 6-quart pan over medium heat, stir onions often in olive oil until limp, about 10 minutes.
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.
Working in small batches, transfer soup to a blender or food processor and whirl until smooth. Pour into a large bowl.
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.