Heat broiler. Using a heavy, sharp knife, slice the mango lengthwise around each side of the pit. Remove the skin and cut the fruit into bite-size pieces. Divide between 2 small ramekins and stir in the lime zest. Top with the yogurt and brown sugar and dot with the butter. Spritz with the lime juice.
Broil 2 to 3 minutes or just until the topping melts and browns.