Preheat the oven to 350°F and place the rack in the center.
Mix cookie crumbs, melted butter, and sugar, press into a tart pan, and bake for 8 minutes until set.
Heat cream and milk over medium heat until steaming, not boiling.
Remove from heat and whisk in chocolate, cocoa powder, vanilla, and salt until smooth.
Let the mixture cool slightly, then whisk in eggs until fully combined.
Pour filling into the crust and bake for 25 to 28 minutes until edges are set and the center slightly wobbles.
Top with marshmallows and broil for 1 to 2 minutes until puffed and lightly golden.
Sprinkle peppermint and shaved chocolate on top, then cool completely before slicing.