Cut out a round from parchment paper to fit just inside a 12-inch heavy skillet (3 inches deep), then set round aside.
Cut peel, including all white pith, from oranges with a sharp paring knife. Working over a bowl, cut segments free from membranes, letting segments fall into bowl, then squeeze 1/2 cup juice from membranes into another bowl (discard membranes). Chop orange segments and reserve.
Cut a 1-inch-thick diagonal slice from a carrot and set aside, then roll carrot away from you 90 degrees and cut another 1-inch-thick diagonal slice. (Shape will resemble a trapezoidal log. If carrots are very thick, cut slices in half lengthwise as well).
Cut up rest of carrot in same manner, then repeat with remaining carrots.
Heat oil in skillet over moderate heat until hot but not smoking, then add cumin seeds and cook, stirring, until fragrant, about 1 minute.
Add carrots, water, orange juice, lemon juice, sugar, salt, and pepper. Cover carrots directly with parchment round and simmer, stirring occasionally, 30 minutes.
Remove parchment, then continue to simmer, stirring occasionally, until most of liquid is evaporated and carrots are tender and glazed, about 20 minutes more.
Serve warm or at room temperature, sprinkled with chopped orange.
Carrots can be cooked 3 hours ahead and chilled, covered. Bring to room temperature before serving.
