It's a Moen Faucet. The good news is the stem is still sold. Lowes or Home Depot. The bad news is when you tried to remove it came apart. The rest of the stem is still in the faucet. They make a tool to remove the rest of it. It's a T shaped handle with a spring loaded pin, that when inserted into the remaining stem it locks into a hole in the stem. Then just twist and pull.
Good luck John