In a large heavy bottom pot heat the olive oil. Add the onions and garlic and sautee on low heat until soft, about 5-7 minutes. Add the carrots and saute a few minutes more. Add the turnips and broth or water and bring to boil, then lower heat and simmer unti turnips are very soft and easily pierced with a knife.
Remove pot from heat and, using an immersion blender or in a food processor, puree soup until smooth. Return pot to stove and add in the dried herbs and salt to taste. Heat soup gently and grate some black pepper across each bowl before serving.