Trim and scrub or peel the carrots and parsnips. If the parsnips are thick, slice them in half or quarters lengthwise so they are about the same width as the carrots.
Place the carrots and parsnips in a pot or Dutch oven, such as Le Creuset, that's large enough for the vegetables to lie flat. Add the shallots, orange zest, 3/4 cup of the orange juice, the olive oil, thyme, red pepper flakes, 2 teaspoons salt, and 1/2 teaspoon black pepper.
Place the pot on the stove and bring to a boil over medium-high heat. Cover tightly with a lid or heavy-duty foil. Transfer to the oven and cook for 1 1/2 hours, until the carrots and parsnips are very tender. Discard the thyme bundle. Sprinkle with the remaining 1/2 cup of orange juice and the parsley and season to taste. Serve hot, warm, or at room temperature.