You have the circuit diagram slightly wrong. The collector winding is connected to the battery terminal, not the resistor. The windings should be opposite polarity, not the same.
simulate this circuit – Schematic created using CircuitLab
It's a pity that the circuit editor only comes with a co-phased transformer, as this wiring looks untidy.
The output comes from magnetic energy stored in the core of the inductor, operation usually described as a flyback. Being an inductor, the output tries to rise to whatever voltage is required to push its current through the load. It's therefore best to call it a current source. That's why it makes a good LED driver.
During the transistor on phase, the current builds in the inductor, and at some current (supply voltage dependent) the on phase finishes. This current now flows through the output, decreasing as the voltage on the load ramps it down again. Calculating the average current is quite complicated as it depends on the on and off time, which depends on the load voltage. So the average output is not truly constant.
In addition to forcing current through the load, it also has to charge the various stray capacitances. With a very large load resistor, these capacitances may dominate the maximum voltage that could be obtained. With a high enough output voltage, the transistor will break down, so this circuit should newer be run without a load.