Preheat oven to 350 degrees F and line a baking sheet with parchment paper and set aside.
Add wet ingredients (sugar, oil, extract and, nut milk) to a bowl and mix with a whisk.
Add flour and salt to wet ingredients in increments and mix with a spatula until a dough forms.
Roll dough into a log and cover with plastic wrap, and place in the refrigerator for 10 minutes to firm.
Remove from refrigerator and cut cookies into 1/4 inch thick and place on the lined baking sheet. Bake for 12-15 minutes until golden brown on the edges. Let rest on a pan for a few minutes, then transfer to a cooling rack to cool.
While cookies are cooling, melt chocolate over a double boiler or in the microwave mixing in increments over 1 minute.
Dip the cool shortbread cookie into the melted chocolate and sprinkle the crushed peppermint on top. Place cookies in a refrigerator to harden the chocolate for 5 minutes before enjoying!