The word double implies two steps. The first step is always going to be the oil cleansing. Oil cleansing can be used to clean the eye. It can also be used to clean the eye if you happen to wear eye makeup.
The second step is going to be primarily a water based cleanser. That's the final wash off. I prefer foaming style cleansers.

First, the positives and then the negatives. I'm a firm believer that a healthy eyelid skin barrier is going to be an eyelid that's going to be less prone to flare ups. Eyes are so unique. The tears inside the eye like to be a pH of 7 which is a neutral pH. The eyelid skin that actually interfaces right next to the tear film, that pH tends to float around closer to a pH of 5. Skin likes to be more acidic.

NUMBER 1. You can use a cleansing oil to clean the eye area. It doesn't contain any surfactants. This means that the cleansing action will not change that pH and that is vital when the tears want a ph of 7 and the eyelid skin wants a pH around 5.

Take a bar of soap – that pH tends to float around 9 or 10, quite a basic pH number. Even take baby shampoo.  Baby shampoo pH tends to float around 6 or 7 which helps it be more "tear less" but ultimately too basic in pH to keep the eyelid skin happy over time. That's why cleansing oils are ideal. It allows the eye area to be cleansed without fussing or messing with the pH that it prefers: tears at 7 and eyelid skin around 5.

NUMBER 2. Cleansing oil is a rock star. When it comes to cleaning the eye area, there's sebum, oils, dirt, debris and also eye makeup. 

Let me show you. I'm a total fan of oil cleanse oil. You add cleansing oil. Here, this is waterproof eyeliner and here we are instantly breaking molecular bonds. This is the cleansing oil step. If you wear a lot of eye makeup, you'll just need to add more cleansing oil. So let's rub that in. Get that nice and clean

Now, we've added the foaming cleanser as the second step. The foaming cleanser is water based and contains surfactants. It will remove lipids, but it's actually removing the lipids of the cleansing oil and not the lipids of that eyelid area. And then you do your final wash off, and there you go. That's how the double cleanse method is done.

TWO. Cleansing oils can clog oil glands, especially if they are 100% of one ingredient. To solve this, always use a blended formulation for your cleansing oil. 100% coconut oil is trending for oil cleansing. 100% coconut oil works for some of my patients, and 100% coconut oil also doesn't work for most of my patients. So just keep that in mind.