A frozen substance maker includes a heat pump, a cold plate, a mold base, a mold top, and an agitator. The cold plate is in thermal communication with the heat pump. The mold base is positioned on the cold plate. The mold base and the cold plate define a seed crystal chamber. The mold top is positioned on the mold base. The mold base and the mold top define a mold cavity in fluid communication with the seed crystal chamber. The mold top defines an overflow reservoir in fluid communication with the mold chamber. The agitator is located at least partially within the overflow reservoir.