Line a 9-by-13-inch baking pan with parchment paper.
To make the base, melt the chocolate and oil in a microwave-safe bowl, stirring until smooth. Add the crushed biscuits and stir until evenly coated. Press firmly into the prepared pan and freeze until set, about 15 minutes.
Meanwhile, make the coconut layer. In a medium bowl, stir together the coconut, sweetened condensed milk, and vanilla until evenly combined. Spread over the chilled base in an even layer.
For the topping, melt the chocolate and oil in a microwave-safe bowl, stirring until smooth. Pour over the coconut layer and spread evenly to the edges.
Freeze until firm, at least 3 hours or overnight.
Cut into squares and serve chilled.