Lasers have come a long way in the past ten years. Before, we could only use very low energy settings. This is because we had no way to contemporaneously cool the tissue as we created a local destruction, or as we heated adjacent structures in the skin-like blood vessels and pigment. We needed some way to cool the surrounding tissues, so as not to create more damage as we targeted unwanted structures. This has allowed us to treat a number of conditions that we were previously unable to. However, we're still greatly limited in our technology by the depth that these lasers are capable of penetrating.
In other words, I can use my strongest, highest frequency wavelength laser, and still only get a few millimeters into the skin. This means that it can be a real challenge to treat deeper lesions like the congenital birthmark that you've described. When you're looking at treating moles that are as big as the one you've defined, another concern is the number of sessions that would be required to lessen the birthmark.
You and your board-certified dermatologist should thoroughly discuss what your expectations are and any concerns that you may have. How long will the treatment take? Will I be looking at a lightened birthmark or one that's entirely removed? These are important questions to ask.
In our practice, we can lighten congenital birthmarks, but not all the time. More importantly, I never go into a patient room with the expectation that I'm going to remove that birthmark entirely. This is because we don’t have the technology to guarantee that.
Other options for birthmark removal include subsequent grafting by a plastic surgeon. This is a very invasive option, but is one that, depending on the size and location of where your birthmark is, is worth considering.