Heat the oil in a large, deep skillet over medium-high heat. Add the shallots and green curry paste. Cook, stirring, until the shallots are soft, 2 to 3 minutes. Add the coconut milk and chicken broth and bring to a simmer.
Stir in the corn and halibut. Cover and simmer over medium heat until the fish is opaque throughout, 6 to 8 minutes.
Spoon the curry over the cooked rice in serving bowls and top with a squeeze of lime and the basil and jalapeño.