Rinse and dry your peppers
When warmed to broil, you are going to put your peppers in, make sure they are in the upper third of your oven (near your broiler). Now you are going to stay in the kitchen because you must watch them very closely since your going to periodically go to rotate your peppers. (as the skin starts to turn black). You're going to continue on all sides until down.
As they get down your going to have your brown bag right there to put them into as they finish roasting. Make sure you put the bags in some sort of pyrex glass dish since there is a lot of juice from the peppers and it will seep out of the bag.
When they are done you are going to close the top of the bag and let them rest. In this cooling down period, their skins are loosening. You're going to wait till their cool and easy to handle.
Make sure you put on a pair of surgical gloves. You do not want your hands discolored from the peppers which will happen if gloves are not used. The skins should easily peel off; try to preserve the juice from the pepper since its practically its own olive oil. This will only give more favor to your peppers. After your all done peeling (you're going to divide them into stripes (the natural sections of the pepper).
Next, you're going to chop your garlic very fine and also your basil. You're going to add your olive oil; I usually do not use any type of vinegar since I like all the true flavor of the peppers and garlic to come through. If you prefer it then, by all means, add it sparingly. You're going to mix it very well and then refrigerate.
Discard the bag with skins and seeds. be careful to not spill it since it can be very messy.