Arrange racks in top and bottom thirds of oven. Preheat to 400 degrees F. Line 2 large rimmed baking pans with foil.
Peel and trim carrots and parsnips, leaving about an inch of the carrot tops, if desired; slice each in half lengthwise--or quarter lengthwise if larger than 1 1/2 inches in diameter.
Whisk together apple cider, cider vinegar, maple syrup, olive oil, black pepper, salt, and cayenne pepper in a very large bowl. Add carrots and parsnips and toss to coat. (This can be made to this point up to 1 day ahead. Cover bowl and refrigerate.)
Divide vegetables and liquid evenly among prepared pans, spreading in a single layer. Roast, stirring twice and rotating pans between top and bottom racks once, until vegetables are tender and browned and liquid has evaporated, about 35 minutes. Garnish with additional fresh thyme.