Squeeze juice from 10 oranges to get about 2 1/2 cups of juice and set aside. Cut remaining 2 oranges in half and scoop our pulp, preserving shape of peel. (You can use the pulp to increase the juice amount if necessary). Place hollowed orange halves in freezer until frozen, about 1 hour.
Melt honey in a small saucepan over low heat until liquefied, about 5 minutes. Remove from heat and stir in 1/4 cup of the orange juice, then stir in remaining orange juice. Place in refrigerator to chill several hours or overnight. Freeze sorbet base in a machine according to manufacturer's instructions. When ready, scoop sorbet into frozen orange cups and garnish with mint leaves.