The dark spot we see is not just the entire event horizon, but the entire event horizon nested and mapped a huge number of times (but a finite number nonetheless).
We are seeing the opposite side of the event horizon. Many times over.
We "see" the photons which reach our, instruments. So, we see a ring, as photons' paths are curved around the black hole and emerge, visible to us much later, from over the horizon of the event horizon. The ones that fall into the event horizon, we don't see. It's not complicated. But it's not intuitive, either.