In a large, heavy pot, heat coconut oil over medium.
Add the onion, ginger and jalapeño; season with the ¾ teaspoon salt.
Cook, stirring, until the onion is soft and translucent; about 6 minutes.
Add the rice and sauté for another minute.
Stir in the coconut milk and 1¼ cups water.
Bring to a simmer, reduce the heat to medium-low, cover, and cook for 10 minutes, adjusting the heat as needed to maintain a gentle simmer but avoid scorching.
Stir in the shrimp and corn, cover again, and cook, stirring occasionally, until the shrimp is cooked through and the rice is tender; 10 to 15 minutes; add more water by ½ cups throughout cooking, as needed, if the water has been absorbed, but the rice is still too firm.
Remove from the heat and stir in the lime zest and basil; season to taste with salt.
Serve immediately with lime wedges and topped with more basil.