Cook the rice in 350 ml of boiling water with a pinch of salt over low heat, covered, for 20 minutes. Add some brown sugar and coconut milk. Stir and cook covered for another 20 minutes.
Coarsely chop the strawberries, sprinkle with brown sugar and drizzle with lime juice. Leave while the rice cooks.
Put the strawberries on the rice along with the juice. Remove from heat, cover with a lid and let the strawberries warm up a bit, 3-4 minutes. Serve immediately, sprinkled with lime zest.