Turn on your vent hood. This is going to get intense. Toss the chilies into a skillet and toast them over low heat. You don't want them to burn so keep your heat fairly low. They should be done after about 4 or 5 minutes. Let them cool.
Slice your shallots in half. Put them in a cast iron pan, cut side down, over medium heat. Add the garlic. Dry roast until the shallots start to char. While that's happening flip the garlic every minute or so.
When the shallots are charred (check them - there's no other way) flip them over. Keep flipping your garlic. When it's all soft remove from heat and let cool. Remove the peels on both the garlic and shallot.
Now the fight starts. It is not easy to puree this stuff. You can use a small food processor. That works. Kind of. Or you can grind manually in a mortar and pestle. That works better.
Sometimes, when I'm using a food processor I give up and add the oil into the mix. Technically you are supposed to fry the paste in oil. But I find when you start cooking it off some of the oil comes out. And your goal is to get the oil into the paste anyway.
Once you have pureed it pour the oil (if you haven't already added it to the paste) into a small frying pan and heat over medium low heat.
When the oil starts to shimmer add the paste and fry, stirring regularly, for about 4-5 minutes. It will darken a bit and start to give off quite a rich aroma. When you get the aroma it's done. You will get it when you get there.
Alternately, If you added the oil to get the paste to puree transfer it to a dry pan and cook over medium low heat as above.
Nam prik pao stores well in a small jar for weeks in the fridge.