Heat oven to 400° F. Wrap each beet in a sheet of aluminum foil. Roast for 1 hour.
Meanwhile, halve the carrots lengthwise, then cut them into 2-inch pieces. Cut each fennel bulb into eighths. In a roasting pan, combine the carrots, fennel, 2 tablespoons of the oil, 3/4 teaspoon of the salt, 1/4 teaspoon of the pepper, and enough water (about 3/4 cup) to measure 1/4 inch deep. Cover with foil and roast for 15 minutes. Uncover and cook until tender, about 15 minutes more; let cool.
Remove the skin from the beets, place them on a cutting board lined with plastic wrap, and cut into quarters. Transfer the vegetables to a platter.
In a small bowl, whisk together the honey, vinegar, and the remaining oil, salt, and pepper. Drizzle the vinaigrette over the vegetables and sprinkle with the parsley. Serve warm or at room temperature.
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