Melt the chocolate chips in a medium bowl set over a double-boiler, stirring with a rubber spatula, until almost entirely melted, about 3 minutes.
Remove the bowl from the heat and continue to stir until the chocolate is completely melted, another 30 seconds. Stir in the hazelnut spread. Let cool slightly.
Preheat the broiler to high.
If the madeleines have a side with a bump, trim the bump to create a flat surface. Cut each madeleine in half horizontally and place cut-side up on a baking sheet. Broil until toasted and brown, 3 minutes. Let cool completely.
Spread a heaping teaspoon of the chocolate mixture evenly over the bottom half of a madeleine; sprinkle with hazelnuts. Place the top half on the hazelnuts and press gently. Dip the assembled madeleine halfway in the chocolate mixture, then place on a tray. Continue with the rest of the madeleines. Refrigerate until completely cool and the chocolate has hardened slightly, 30 minutes.
Serve alongside Bourbon Milk (see below) if desired.