Peel carrots, potatoes and onions and cut into thin strips. Heat vegetable oil in a saucepan. Stirring constantly, fry vegetables, 6 minutes. Pour in the broth and bring to a boil over high heat. Reduce heat and cook 10 min.
Pour the contents of the saucepan into a blender bowl and grind to a puree. Return puree to saucepan, season with salt and pepper to taste. Heat through without boiling.
Wash dill, dry. Grind greens and pine nuts in a blender. With the blender running, pour in the olive oil in a thin stream. Salt to taste. Add pesto to soup.