Heat 1 tablespoon oil in a heavy pot over medium-high heat. Add onions, curry paste, and garlic and saute until onion is softened, 3 to 4 minutes. Make sure to mix well. Add chicken breasts, water, and russet potato. Reduce heat to medium-low and cook for 40 minutes.

Meanwhile, heat remaining oil in a pan over medium heat. Add sweet potato and 1/2 teaspoon sea salt and toss to coat with oil. Cook, tossing frequently, until potatoes start to brown on the bottom, 5 to 7 minutes. Set potatoes aside.

Add coconut milk, carrot, turmeric, sugar, soy sauce, and remaining sea salt to the pan. Stir and return to a simmer, about 5 minutes. Stir in lime juice and season with additional salt, if desired.

Serve curry with a scoop of sweet potatoes on top of jasmine rice.