In a saucepan, bring water to a boil. Stir in rice and salt and return to a boil over medium-high heat.
Reduce heat to a simmer, cover, and cook until rice is tender and has absorbed all the liquid, about 16 to 18 minutes.
Remove from heat and let steam, covered, for 10 minutes.
In a large skillet, heat olive oil over medium heat. Add onion and salt and cook until onion turns translucent, about 4 minutes. Add ginger and garlic and cook until fragrant, about 30 seconds.
Add red bell pepper and carrots. Cook until fork-tender, about 4 minutes, stirring occasionally. Stir in Thai curry paste and cook for about 2 more minutes.
Add coconut milk, water, kale, brown sugar, and combine. Bring mixture to a simmer over medium heat. Reduce heat as necessary to maintain a gentle simmer and cook until peppers, carrots and kale have softened, about 5 to 10 minutes.
Remove from heat and season with soy sauce and lime juice.
Using a fork, fluff the rice. Divide rice and curry evenly among 4 bowls. Garnish with cilantro.