In a large saucepan, heat the oil over moderately low heat.
Add the onion and cook, stirring occasionally, until translucent, about 5 minutes.
Stir in the garlic and jalapeño and cook, stirring, until fragrant, about 30 seconds.
Stir in the kale, sweet potatoes, broth, and salt and bring to a boil.
Reduce the heat and simmer, partially covered, until the potatoes are tender, about 20 minutes.
Add the coconut milk and just heat through.
Meanwhile, bring a medium pot of salted water to a boil.
Stir in the rice and boil until just done, 10 to 12 minutes.
Drain.
Put a mound of rice in the center of each bowl.
Ladle the soup around the rice.