Preheat broiler. Prepare rice according to package directions.
Add milk, 1 cup brown sugar and butter to rice. Bring to a gentle boil, stirring frequently. Reduce heat and simmer 10 minutes, stirring occasionally. Beat egg yolks in a small bowl. Add 1/2 cup rice mixture to yolks and beat vigorously. Pour the warmed egg mixture back into the pot. Remove from heat and continue to stir until the pudding is thick and creamy, about 1-2 minutes. Pour pudding into 4 oven-proof dishes.
In a mixing bowl, beat egg whites until soft peaks form; gradually add remaining 1/4 cup of brown sugar. Continue to beat until stiff peaks form. Spread meringue over each pudding.
Put puddings on a cookie sheet and place under broiler. Watch carefully and remove when tops are lightly browned, about 1 minute. Serve warm.