What's the best way to crack open a Brazil nut without breaking the nut?

Microwave them. My microwave is 820W, so adjust the time according to the wattage of your microwave. Have a bowl of cold water near, as the nuts will be hot. One brazil nut = 30 seconds on high. Drop the hot nut in the cold water for a few seconds, just until it's cool enough to handle. Use a nut cracker and gently crack it slightly. Put it back in the cold water until the nut inside is cool, or not if you want warm nuts, which are tasty as well. You may need to used the cracker again, but the nut should come out whole.

If you own a vise, there's a very easy way. First, freeze the nuts for an hour or two. Then put them in your vise and squeeze the nut on the ends. Turning the vise handle allow precise, specific pressure on the shell while avoiding damaging the seed. I did a 1lb bag in 10 minutes.

****No soaking, no freezing, no boiling**! We had Brazil nuts that stuck to the shell so tightly that after they were cracked, they had to be scraped off the shell with a knife. I found that 30 seconds in the microwave before cracking them released them from the hull and every nut came out whole.

No need to follow the complicated instructions in the other responses. However, skip the nutcracker - you will need better tools.

I use a tongue-and-groove pliers set to the widest position that still "bites" to create an initial crack in the nut. After that I use a quite narrow regular, flat, screwdriver to widen the crack the pliers created, either by pushing in the screwdriver in the crack and rotate it or pushing it in between the kernel and the shell and bend.

Hard to describe the direction I insert the nut in the pliers, but if you think at is as an orange cleft, you place the narrow edge that is located towards the centre of the fruit and the wide edge that is next to the peel in the pliers.

This way 70-80 % of the nuts opens with the kernel in one piece.

I use 45 seconds in a 1250 watt microwave, then, being careful not to burn my hand on the hot nut, crack carefully along the to seam using adjustable vice-grip pliers adjusted so that they don't crush the kernel when the shell breaks and the pliers slam shut.

3 or 4 cracks that way usually opens it up enough to extract the kernel intact. The microwaving seems to release the kernel from being stuck to the shell so that it comes out fairly readily. The vice-grips give you plenty of leverage if you use a large one and its adjusting feature lets you exert as much force as needed without concern that when the shell breaks, you would overshoot and crush the kernel.

A rubber band wrapped several times around the end of the handle and holding down release lever prevents the pliers from locking closed, allowing you to sort of "nibble" your way along the nut's seam without having to let go and release the pliers before taking the next "bite". The workshop vice, suggested above, would have the same advantage, but most people don't have one mounted on their kitchen table.