Turns out this is a cactus fruit that's very sweet and wonderful and non-stinky. There are several varieties, some white on the inside like this one, and some red, with tiny, edible black seeds. I had to do some googling to figure out what to do with it (besides admire it). It's actually really easy to just slice it in half, scoop out the fruit with a spoon, and cut it up.
Place the fruit back in the shell for an exotic serving bowl. Dragon fruit is delicious all by itself, and we also liked it with a little bit of Strawberry-Balsamic Reduction Sauce. I think a squeeze of lime would be nice too. If you see this crazy fruit in the store, buy it! It might not become a staple in your house, but it's certainly something worth experiencing at least once.
