When you disconnect a small voltage battery from a coil of many loops of wire and a large voltage is produced by what?

Disconnecting a small voltage source from a coil (inductor) causes a larger, often a much larger, reverse voltage spike due to the collapse of the magnetic field in the inductor coupled with the sudden absence of a current path to dissipate the electromagnetic energy.

An inductor resists a change in current. The equation for an inductor is ...

di/dt = V/L

... which means that the rate of change of current is proportional to voltage and inversely proportional to inductance.

If you have a current established in an inductor, and then suddenly open the circuit, the inductor will attempt to maintain that current. It can't, however, because the circuit is open, having large resistance. By ohm's law, voltage is resistance times current. If you keep current constant, and make resistance large, then voltage has to also be large.

In the theoretical case of an ideal inductor in an ideal circuit, the voltage spike would have infinite voltage. In practice, we see spikes of several hundred to several thousand volts, depending on the particular cirsumstances.