Heat is your friend; also PB blaster penetrating catalyst. Alternatively mix together a small amount of transmission fluid or hydraulic fluid with acetone, it works just as well, with an eyedropper, drip into or onto all rusty, seized surfaces and let it sit. Regarding the heat, you want to generate expansion and contraction cycles, so heat the bolt and surrounding area with a propane torch and take an ice cube and hold it to the tip of the broken-off bolt to cool and contract it faster than the surrounding metal. Spray a little of the hydraulic fluid mix into the boundary area. NOTE: a little bit - the acetone will likely ignite so be careful !!! Keep your container of fluid or PB blaster, whatever you are using away from your work area. If it doesn't break loose then try again and increase the heat - get the bolt good and hot forcing it to expand; red hot if necessary. Then cool it.
If after two or three cycles, increasing the heat if the first attempt doesn't work, you are going to drill and tap as said above by Broncobowsher. But at least you have probably annealed the bolt and it may drill more easily. I've had much better results drilling and tapping than with easy outs. Also - BE VERY PATIENT !!! Removing a broken easy out or tap may mean you will have to weld a nut to the easy out or tap fragment (you are essentially creating a head to a bolt) to remove it as they will be hardened and that is a whole new problem. Unless you are lucky and can grab it with vise grips, but if you were lucky the bolts wouldn't have broken in the first place.
Wishing you luck though !