Yes, it's called a saturable reactor [0] and can be considered as a very simple type of magnetic amplifier. You control the impedance of the reactor using the extra winding, conceptually similar to how you control the conductivity of the pass transistor in a solid-state voltage regulator. You can find them in old Tektronix oscilloscopes, here's a long (70 min.) and comprehensive video [1] on the design of the Tektronix 555 power supply, including the operation of the saturable reactor voltage regulator.

[0] https://en.wikipedia.org/wiki/Saturable_reactor

[1] https://www.youtube.com/watch?v=CAbeWXcuYOE