Best way to remove & retap broken bolts?

I have a couple of broken off 10mm bolts that secure the plastic or metal shields under the front end. I'm guessing those were never removed and I'm in the midwest rust belt so they broke off right after the washer. The
remaining part is still in the threaded hole. There is no tip sticking out on any of them.
What's the best way to get the rest of the bolt out and put in a new bolt? I've heard about the easy out bits but these bolts seems really small so I don't know whether it's appropriate. I don't want to destroy the threaded part if possible. Drilling it out?
How do you guys fix these?
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Drill another hole next to it and fasten with a nut and bolt.
If removal is absolutely necessary, I'll first attempt to weld a nut on the broken stub with my MIG welder (works 99+% of the time) and back it out with a wrench, if that fails, drilling the broken stub out is the only other option. Easy-outs are an exercise in futility.
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If you can get a drill on it at a straight shot (center and proper angle) then center punch the broken bolt. drill down the center with a 1/8 titanium tip (or good quality drill bit) then go larger to almost then entire bolt size. Get a sharp awl and pick out the remaining steel in threads or us a tap the proper sze to chase the threads. Not fun. Try squirting for several days in advance next time with Liquid Wrench.
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