In a medium saucepan over medium heat, add heavy cream, milk and sugar. Stir until sugar is dissolved heat the mixture just before it starts to simmer (between 160ºF to 170ºF).
Turn off the heat, add mint leaves, stir, and let the mixture steep for 2 hours, stirring occasionally. Strain the mixture through a fine sieve sitting over a bowl, pressing down the solids with the back of a wooden spoon; discard the mint leaves.
Pour the mixture back into the saucepan and return to the stove. Warm up the mixture on medium heat.
Meantime, add yolks to a medium bowl and whisk until nicely beaten; set aside.
When it reaches around 140ºF, ladle some up and slowly pour in a tiny amount at a time to the yolks, whisking constantly.
When the yolks are tempered, add them to the saucepan and whisk continuously.
When the custard temperature reaches 170ºF, remove from the heat and pass it through a fine sieve sitting over a bowl or a large measuring cup; discard any cooked eggs if there are any.
Add vanilla seeds and a small pinch of fleur de sel; whisk until well blended.
Place a piece of wax paper on top making sure it touches the surface and let it cool off about 30 minutes before transferring it to the fridge to chill overnight.
The next day, pour the chilled custard into the bowl of an ice cream maker and process according to the manufacturer’s instructions.
About halfway through churning, add shaved chocolate.
A couple minutes before it’s done, add Crème de Menthe and a few drops of food coloring; continue churning. When the desired consistency is reached, spoon the mixture into a 2-quart container, place a lid on and transfer to the freezer until frozen, about 4 hours.