Heat the oven to 350°F. Bring a large pot of water to a boil, then reduce the heat to medium. Cut the carrots into 2-inch pieces. Cook the potatoes in their skins for 20 minutes, adding the carrots after 10 minutes. Drain in a colander; set aside until cool enough to handle.
Peel the potatoes and cut into 1-inch chunks. Transfer the potatoes and carrots to a large bowl.
In a medium skillet over medium heat, melt the butter. Add the dates, apricots, apple, if using, cherries, if using, orange juice, syrup, lemon juice, and brown sugar and simmer for 1 to 2 minutes, just until heated through. Transfer to the potato mixture and stir well to combine.
Add the parsley and salt and toss well to combine. Transfer to a 2-quart baking dish. Cover and bake, basting after 15 minutes, for about 30 minutes total, until the potatoes are fork-tender and juices are bubbling.