How to Make It
Preheat the oven to 400°. Put the beets and garlic on a large piece of foil and sprinkle with the water. Wrap the beets and garlic in the foil and roast for about 1 hour, or until the beets are tender when pierced with a knife and the garlic feels soft when pressed. Let cool slightly. Peel and quarter the beets and put them in a large bowl. Squeeze the soft garlic cloves from their skins onto the beets.
Meanwhile, on a large rimmed baking sheet, toss the carrots, turnips and onions with 1 tablespoon of the olive oil and season with salt and pepper. Spread the vegetables in a single layer and roast for about 1 hour, stirring occasionally, until tender and browned. Add the roasted vegetables to the beets.
Arrange the baguette slices on another baking sheet and bake for about 3 minutes, or until toasted.
Working in batches, coarsely puree all of the roasted vegetables in a food processor, adding enough chicken stock to loosen the mix. Transfer the puree to a saucepan, add the remaining chicken stock and bring to a simmer over moderate heat. Season with salt and pepper.
In a small bowl, stir the remaining 1/4 cup of oil into the mint and season with salt and pepper. Spoon the mint onto the toasts. Ladle the soup into bowls and serve with the mint croutons.