1. Prepare the Crust:

1. Cut the top third off each lemon and carefully hollow out the insides, removing all pulp and juice (reserve juice for posset). Trim a small slice off the bottom of each lemon shell so they stand upright.
2. In a saucepan, combine heavy cream and granulated sugar. Bring to a gentle boil over medium heat, stirring until sugar dissolves. Reduce heat and simmer for 3 minutes, stirring occasionally.
3. Remove from heat and stir in fresh lemon juice and lemon zest. Let mixture cool for 10 minutes, then strain through a fine-mesh sieve into a jug.
4. Pour posset mixture into prepared lemon shells, filling each about 3/4 full. Chill in refrigerator for at least 4 hours, or until set.
5. For pistachio sand, combine chopped pistachios, brown sugar, and melted butter in a bowl. Mix until crumbly. Toast in a dry skillet over low heat for 2-3 minutes until fragrant, then let cool.
6. Before serving, sprinkle pistachio sand over set posset in lemon shells. Garnish with fresh mint leaves.