Grease and line a 9-inch square baking pan with parchment paper, creating a sling for easy removal.
In a food processor, pulse graham crackers, sugar, cocoa, and salt until fine crumbs form.
Transfer crumbs to a bowl, add coconut and melted butter, then mix until the texture resembles wet sand.
Press the crust mixture evenly into the prepared pan, then freeze for 20 minutes to set.
In a medium bowl, combine confectioner’s sugar, butter, peppermint extract, vanilla bean paste, and salt.
Add boiling water gradually, mixing until the filling is a thick, smooth paste, adjusting water as needed.
Remove crust from freezer, spread peppermint filling evenly over it, then chill for 30 minutes until set.
Melt dark chocolate and neutral oil together over simmering water or in short microwave bursts until smooth.
Pour chocolate topping over the set peppermint layer, tilt pan to coat evenly, and tap to remove bubbles.
Chill in the refrigerator for at least one hour until completely firm.
Use parchment sling to lift slice out of pan and cut into 24 pieces, wiping knife between cuts.
Store peppermint slices in an airtight container.