Mix carrots and orange juice in a large saucepan; bring to a boil, place a cover on the pan, reduce heat to low, and cook at a simmer until carrots are tender-crisp, 8 to 10 minutes. Drain carrots, reserving 1/4 cup of the orange juice.
Return carrots and reserved juice to the pan and place over medium heat. Stir honey, apricot preserves, Dijon mustard, butter, brown sugar, salt, and black pepper with the carrots and juice; cook and stir until sugar dissolves completely and the carrots are glazed and tender, about 10 minutes.
