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Step 1
Place a rack in the center of the oven and preheat to 350 degrees F. Very lightly spray two 8-inch round cake pans with cooking spray and set aside.
Step 2
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter, 1/2 cup of the sugar, the nutmeg, cinnamon and salt together on low speed. Once combined, increase the speed to medium and beat until very smooth, about 1 minute.
Step 3
Scrape the sides of the bowl and the paddle with a rubber spatula and add the rum and vanilla. Beat on medium speed until combined, about 30 seconds. Add the flour and mix on low until uniformly combined. Scrape the bowl and paddle and then use your spatula to give the dough one final mix to ensure that everything is evenly combined.
Step 4
Divide the dough in half and place one half in each prepared pan. Use your hand to spread and flatten the dough to evenly cover the bottom of each pan. If the dough sticks, coat your hand in some granulated sugar.
Step 5
Whisk the egg yolk and cream together in a small bowl. Use a pastry brush to brush the egg wash over the dough (you won't use all of the egg wash). Avoid brushing the egg wash onto the edge of the pan. Sprinkle each pan with 1 1/2 tablespoons of the remaining granulated sugar. Use a fork to pierce the dough all over. Optionally, use an approximately 1-inch round cookie cutter to remove the center bit of dough; this will help the shortbread bake evenly and prevents breakage when cutting.
Step 6
Bake both pans side-by-side on the center rack of the oven until golden brown, 45 to 50 minutes, turning the pans about halfway through baking to ensure even browning. Allow the cookies to cool in the pans for 15 minutes, then turn them out onto a cutting board and slice each disk into 12 wedges. Transfer the wedges to a parchment-lined baking sheet.
Step 7
Melt the white chocolate chips in a small microwave-safe bowl in 10-second intervals, stirring between intervals, until smooth. Spoon the melted chips into a small resealable sandwich bag or small disposable piping bag and snip off the tip to create a small opening. Drizzle the chocolate over the warm shortbreads. Enjoy warm or room temperature. To store the cookies, allow them to cool and place them in an airtight container for up to 1 week.