What can be known?

It seems to me that there is a fundamental truth about what can be known. By that, I don't mean how many areas one can be an expert in, or how many trivia facts a human's brain can hold. I'm talking about the edges of what an intelligence can learn about reality itself. That truth is the following:

There are two possibilities: there is an end to what is knowable, or what is knowable recurses infinitely.

I can't seem to think of any logical way there could exist any other options. It almost feels like a tautology, right? It's true by necessity; there's no third option. But where does that leave us?

If it's the former, there's just an end. Quantum mechanics? Yeah, that's it. That's what's going on here. That's the whole universe and everything in it. Oh, you want to know why? There is no why. Deal with it.

If it's the latter, where does that leave a curious mind? Good luck, your inquisitiveness leads nowhere. Even if you research till the heat death of the universe (or all of the universes in the multiverse. Or throughout every repeat of time.) you'll never get it. There's always another layer.

I don't think I like either option, but I don't think there's much of a choice in the matter. This reality isn't particularly satiating to the curious.