Remove the specified amount of zest from the oranges, then peel with a sharp knife, removing all the white pith.
Remove the membrane from each segment, and place the segments in a bowl.
In a small saucepan, dissolve the sugar in the water and boil for 2 minutes. Remove from heat, add the orange zest, orange liqueur and vanilla. Pour the hot mixture over the orange segments and let sit for 2 hours.
Add the mint strips and stir gently. Serve garnished with mint sprigs.