Heat the oven to 350 degrees F. Cut the carrots and parsnip on the diagonal into 1-inch chunks. Cut the turnips and onions into wedges about 1 inch thick at their widest point. Split the fennel bulb lengthwise, notch out the core, and then cut the fennel crosswise into 1-inch slices. Heat the olive oil
in a medium (9- inch) Dutch oven
over medium heat. Add the onions and cook, stirring occasionally, until softened and lightly browned, about 5 minutes. Add the other vegetables
, the bouquet garni, 1/2 teaspoon salt, and pepper to taste. Raise the heat to medium high and cook until the vegetables are lightly browned, 5 to 7 minutes. Add the water or broth and bring to a boil. Cover the pot, put it in the oven, and bake until the vegetables are fully cooked but still hold their shape, 20 to 25 minutes. With a slotted spoon, transfer the vegetables to a serving bowl
. Bring the pan juices to a boil over medium heat.(If there's a lot of liquid left, boil until reduced to about 1/4 cup
.) Discard the bouquet garni. Whisk in the butter and herbs. Spoon the sauce over the vegetables and serve.