Place the rice and water in a small to medium pot. Bring to a boil, cover, and then turn the heat to its lowest setting. Let rice steam 15 minutes, or until tender.
While the rice cooks, place the coconut milk, cornstarch, curry powder, lime juice, sugar and soy sauce in a second pot and whisk to combine. Bring to a simmer, simmer 2 minutes, and then remove from the heat and reserve.
Place the oil in a wok or very large skillet set over medium-high heat. Add the onion, carrot, broccoli, bell pepper and snap peas and cook 3 to 4 minutes. Add the bok choy and green onion and cook 1 minute more. Pour in the coconut milk mixture, bring to simmer, and simmer 1 to 2 minutes, or until the vegetables are just tender.
Spoon the rice into serving bowls, top with the saucy vegetables and serve.