Blanch carrots in a large pot of boiling salted water until crisp-tender, about 4 minutes. Transfer carrots to bowl of ice water using slotted spoon. Return water to boil. Add sprouts and blanch until crisp-tender, about 5 minutes. Transfer to another bowl of ice water. Drain vegetables, and refrigerate if making ahead.
Bring stock, butter or margarine, and brown sugar to a boil in a heavy large skillet. Stir until sugar dissolves. Boil until reduced by half, about 7 minutes. Can be prepared 6 hours ahead; return to boil before continuing. Add carrots. Cook until almost tender and sauce begins to coat, shaking pan occasionally, about 6 minutes. Add Brussels sprouts and pepper. Cook until heated through, stirring occasionally, about 4 minutes.