Preheat the oven to 400 degrees F.
In a small ovenproof casserole or roasting pan place the beets with 1 tablespoon of the olive oil, 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper. Toss to coat well and push to 1 side of the pan. In a piece of foil, place the carrots with 1 tablespoon of the olive oil, 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper. Toss to coat well. Wrap the foil tightly and place alongside the beets in the roasting pan. Transfer to the oven and bake, stirring occasionally, until the beets are crisp-tender, about 45 minutes. The carrots may be done earlier, so check occasionally. Remove the beets from the oven and allow to cool slightly. Toss with the tarragon and chives and set aside to cool to room temperature.
In a mixing bowl combine the sherry vinegar, honey, remaining salt, and remaining pepper and whisk to combine. While continuing to whisk, add the remaining 1/4 cup of olive oil and the walnut oil in a thin, steady stream, until smooth and emulsified.
Place the lettuce in a salad bowl and add the beets, walnuts, and crumbled goat cheese. Drizzle some of the vinaigrette over the salad, to taste, and toss to thoroughly combine. Serve immediately, drizzled with additional vinaigrette, if desired.