Trim and scrub or peel the carrots and parsnips. If the parsnips are thick, slice them in half or quarters so they are about the same width as the carrots.
Place the carrots and parsnips in a pot or Dutch oven, such as LeCreuset, that's large enough for the vegetables to be flat. Add the shallots, orange zest, 3/4 cup of the orange juice, the olive oil, thyme, 2 t salt and 1/2 t black pepper. You can add a pinch of red pepper flakes, if desired.
Place the pot on the stove and bring to a boil over medium-high heat. Cover tightly with a lid. 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.