In a large bowl, or the bowl of a stand mixer fitted with the paddle attachment, mix butter on medium speed until pale and fluffy. Slowly add confectioners’ sugar, taking time to scrape down sides as you go. Add egg yolk and rum, continuing to scrape down sides as needed.

In a small bowl, mix the sea salt and flour.

Turn mixer to low, and slowly incorporate the flour mixture, orange zest, and nutmeg. Mix just until dough starts to clump up and holds together when squeezed.

Turn dough out onto a lightly floured surface and gently knead into a large mound. If dough is too crumbly, add a drizzle of ice water. Divide dough into 2 discs, wrap tightly with plastic wrap, and set in fridge to chill for at least 2 hours.

Preheat oven to 350 degrees. Line 2 baking sheets with parchment paper.

Remove 1 dough disc from fridge and set out for 20 minutes or until dough is workable. On a lightly floured surface, roll dough into a large rectangle, about 1/4-inch thick. Use cookie cutters to create shapes, placing cutouts on prepared baking sheets. Gather scraps, re-roll, and cut until you’ve used all the dough.

Bake cookies in batches for 11-14 minutes, or just until the edges are a very light golden brown. Cool cookies on the baking sheet for 10 minutes, then remove to a rack to cool completely.

Repeat for second disc.

In a small bowl, mix together confectioners’ sugar, orange zest, 2 tablespoons of orange juice, rum (if using), and nutmeg. Stir until smooth. Use remaining tablespoon of juice to adjust the icing for spreadability, according to your preference.

Drizzle icing on cookies and use the back of a spoon to spread. While icing is still wet, add orange zest and grated nutmeg for garnish.

Allow frosting to harden before storing. Keep finished cookies sealed at room temperature for up to 3 days.