Cut the oranges in half and use a grapefruit knife to cut the flesh away from the skin. Cut the orange segments into bite-size pieces. Spoon a small amount of Drambuie onto the oranges. You don't need too much but may have to experiment on this (one of the perks of being a cook!). You can leave the oranges at room temperature until you are ready to go on to the next stage.
Sprinkle brown sugar on the top of the oranges and grill (broil) under a hot grill until the sugar starts to bubble. Decorate with a sprig of mint before serving.