Preheat the oven to 350 F and prepare two baking sheets with parchment paper.
Place the vegan butter and powdered sugar into the bowl of a stand alone mixer or a large mixing bowl if using a handheld mixer. Beat the butter and powdered sugar together until well combined, about 1-2 minutes. Add in the vanilla extract and mix until combined. Mix in the flour and sea salt until a dough forms.
Seaparte the dough into 14 evenly sized balls and place them on the baking sheets about 1 -2 inches apart. They won't spread. Use the back of a teaspoon sized measuring spoon to press the balls down and make an indent in the center. Bake the cookies for 12-14 minutes. Let them cool on the baking sheet for 10 minutes before transferring to a cooling rack to continue cooling.
Once cooled, melt the chocolate and coconut oil in a heat proof bowl over a small pot of simmering water. Stir the chocolate every so often until completely melted and then remove it from the heat.
Fill the cavities of the cookies with chocolate. Let them cool at room temperature for 10-15 mintues before topping with peppermint candies to ensure the candies won't sink into the chocolate.
Allow the chocolate to continue to cool at room temperature until solid, about 1 hour.