Preheat the oven to 425°F.
Cut the corn kernels off the cobs and put into a large bowl. You should have about 2 cups of kernels. (Feel free to use thawed frozen corn, too, if it’s easier.)
Lay a 3-foot-long piece of parchment paper on a large rimmed baking sheet. (Parchment can be easier to work with if you crumple it first and then spread it out).
Bake the packet for 20 minutes, until slightly puffed. Using scissors, snip open the packet to release the steam (be careful—it’s hot). Using a spoon, transfer the vegetables, halibut, and any juices to a deep platter or four shallow bowls. Scatter the basil and jalapeño evenly on top and serve hot.