First, thanks for your answer and tips!
What is happening I believe you are killing the 3V3 regulator
Do you mean the Arduino regulator?
Secondly, I've already connected a variable power supply to the LED to characterize and what I found is that, given 3.3V, the resulting current drained by the LED is about 0.73 A at maximum brightness (i.e., about 2.5W). You can find the LED I'm using by clicking here.
I know these LEDs are not the best choice, but for now I've to work something out with this one...