It sounds like someone went over the brick w/cement. I could be wrong in that maybe they used a stucco-like material.
If you can take a chunk of it to a local Cement Maker or Block Maker or even Quarry, you may get a better answer. First, as you are doing, you need to identify the material, then, seal it over. For some painful reason, I don't think what you want to do is going to do anything for you. If water wants to 'push' its way into the basement, it will. That's why it's important to have proper landscaping and landscape drainage outside, along with non-leaking gutters, properly installed gutters, gutters where there SHOULD be gutters, and downspouts that dump the water well away from the foundation. 90% of basement water/moisture problems are fixed sufficiently enough by addressing the aforementioned items. If, after that, you still have leakage, then either something was overlooked or you have a high water table.