Line a sheet pan with parchment paper and set aside.
Since white chocolate hardens quickly, it’s easiest to work in several batches: In a microwave-safe bowl, place 1/2 cup white chocolate chips with 1/4 tablespoon vegetable oil in the microwave.
Microwave for 30 seconds, stir, and microwave another 25 seconds. Stir until melted, microwave for a little longer. Add more vegetable oil if needed.
Holding the cookie in one hand and holding a spoon in the other, spoon melted chocolate over the top 2/3rds of the cookies.
Lightly tap the cookies on the edge of the bowl to get a nice even coating of chocolate. (Don’t dip the cookie in the chocolate because the chocolate in the Milano will mix with the white chocolate).
Place the dipped cookies on prepared sheet pan and allow to completely dry.
Repeat with remaining cookies.
Place all the leftover white chocolate (make sure it is still very melted—microwave another 15 seconds if needed) into a small resealable plastic bag (or a piping bag fitted with a #2 tip).
Cut the very edge corner off of the bag, and pipe melted white chocolate over the cookies to form the “bandages” of the mummy.