I have a leaky 2 handle bathroom faucet with the following cartridge below.
What brand is that cartridge/faucet (1st question), and is that so antiquated and old that I should replace the entire faucet (2nd question)? (It does not look like a design I've worked with previously.)
2nd question is more to, "oh no that's a terrible design and you shouldn't bother fixing that type of faucet," etc.. No need to effort replacing if this is not advisable.
Best Answer
Looks like a Price Pfister (or import copy thereof). Looks like a good quality faucet that is worth saving.
Note- you don't necessarily need to buy new "cartridges", these are totally rebuild-able unless physically damaged. The washers and o-rings should be readily available at a good hardware shop or plumbing shop (maybe not at big-box center). Waterproof grease and washers it will probably perform like new.
Look for Price Pfister widespread faucet parts. Bring the old because there are several configurations/types. If replacing stems/valves be aware that there are specific "left" and "right" because the levers move opposite of each other.