I need faucet help

Our kitchen faucet is kind of drippy. I assume it needs a new washer or maybe even a new internal cartridge. I need to know how to open it and get inside. The problem is that it is not obvious to me how to do this.

There is no hidden hex key that I can use an Allan key to open. Seriously. There is not.

If I knew what brand this faucet is, I could maybe find someone on Youtube who'd tell me how to open it. The faucet came with the house. So it's no reflection on it that after 24 years it's hard to turn off. [But still, next time, if I buy a faucet, it will probably be a Moen because there are all kinds of guys who tell you how to replace their cartridges.]

So:

1. Can you tell me what company made this faucet?
2. Can you tell me how to open it?

Thank you.

Update

RealGrouchy and Dana ask about what's underneath. It's not easy to get at, but it looks like this.