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I drilled completely through a manifold stud that broke off, it was recessed about a millimeter.

Now I'm afraid I'll break my extractor off in the hole, there isn't much of the stud left so I was
thinking of using a pick to get it out.

Does anyone have other ideas?

Two options as I see it, based on how it's drilled:

If you can apply heat around the stud remnants to expand the manifold it will probably come right out with your extractor;
Or, use a chisel, and hammer the thicker wall area (about 2 and 4 o'clock) inward-this should collapse the remnants enough for you to get a pair of needle nosed vise-grips or pliers on it and turn it out.

Extractors need to be perfectly centered in a drilled hole to run the least risk of breaking one. You'll also want to use a quality extractor. I'm sure I could remove it if it were in front of me, as I've had lots of practice.

Good luck-let us know how it turns out (no pun intended)!
Gary

With the way it's drilled, I would have to say that your best bet would be a chisel and hammer.

Bert

What about drilling it all the way out and putting a helicoil and a new stud in?

Not sure I'd use an extractor as that metal at 6-8 o'clock looks real thin. I'd be afraid of damaging the threads. Gary seems to have the best idea so far, if it were me, I'd probably grab a Dremel and remove as much as I could that way. Lots of heat and penetrating oil. Whatever you do, chase the threads with the correct tap when you get it out.