Heat the oven to 350 degrees F. Line 2 (12 cup) cupcake tins with silver foil paper liners.
In a large mixing bowl, combine the eggs, cake mix, oil, and chocolate milk. Beat on medium speed for 2 minutes, scraping down the bowl to be sure the batter is well incorporated.
In a microwave, melt 1/2 cup of the semisweet chocolate at 10 second intervals. Add 1 cup batter to the melted chocolate and stir well to combine. Place into a plastic releasable bag and cut off the corner. Take a small ice cream scoop and fill each cup with 1 scoop of cake batter, about one-quarter of the way up the cupcake paper. Pipe about 1 tablespoon batter with melted chocolate in each batter-filled cup. Top each with another scoop of the remaining cake batter.
Bake until a toothpick inserted in the center comes out clean, about 12 minutes. Remove from the oven and cool completely on a wire cooling rack.
To make the icing, heat the cream in a saucepan over low heat to a simmer. Remove from the heat and stir in the remaining chocolate chips until completely combined. While still slightly warm, dip the tops of the cupcakes in the chocolate icing. Place on a wire cooling rack, sprinkle with dragees, and allow the icing to set.