How is it possible to create a hole in an overlay where you can see through to the actual website?
You can now achieve this with relatively good support in new webkit browsers using css clipping (see here for compatability).
For example, the following code would cut a hole with a radius of 100px (so 200px wide) in the center of your element (with a slightly feathered edge).
-webkit-mask-image radial-gradient(100px at 50% 50% , transparent 95%, black 100%)
Here's a codepen to demonstrate.