Slice the shallots so that they're super thin (use a mandolin if you have one, a very sharp knife if not).
Place them in a pan and add oil to cover.
Turn the heat up to high and watch the shallots bubble (first you'll see small bubbles, then more rapid ones will appear): That's the water evaporating off.
Lower the heat to medium, and allow it to continue to bubble. When the bubbles subside, it means that the moisture has cooked off the shallots, and by this time they should be golden brown. This should take around 8 minutes.
Transfer the shallots with a slotted spoon to a paper-towel lined surface or plate and allow to cool completely.