Hi Mateo,
First, because you'll need lots of it, the shade-tree mechanic's penetrating oil recipe:- Equal parts Acetone and Automatic Transmission Fluid.
Works as good or better than propriatory brands at ~1/10th of the cost.
Do NOT use an easyout to try and remove that broken adjuster. It won't work.
It'll snap off in the pilot hole instead and it's busted-off end is harder than any known drill bit.
I'd advise against using a left-hand drill bit, too. You don't want to threat the rest of that rusted adjuster out of the hole, you want to thread it in.
First make a screwdriver slot across the stub's inner end. Then after it's soaked in it's jar of penetrating fluid for a day or two, carefully drill into the busted end with a 3/16" drill bit. This should loosen the stub enough that a screwdriver should turn it. If not, take it out to 13/64" and try again.