In a large bowl, beat the butter with an electric mixer until lightened in color and texture, 1 to 2 minutes. Gradually add the sugar and continue to beat until the mixture is light, about 2 minutes more. Add the eggs and beat until well combined.

In a medium bowl, sift together 3 cups of the flour and the salt, cinnamon, and nutmeg. Add half the flour mixture to the bowl with the wet ingredients and stir to combine. Then add half the sherry and stir to incorporate. Repeat with remaining flour mixture and sherry. When all is well blended, add enough additional flour to stiffen the dough, about 1 cup. Wrap the dough in plastic wrap and refrigerate for at least 2 hours.

Preheat the oven to 450°F. Grease two baking sheets. Flour a work surface and roll out the dough to a mere 1/16 inch thick. Cut out cookies with a cookie cutter. Place on cookie sheets, leaving an inch of space between cookies. You will need to bake in several batches. Bake for about 7 minutes.

Beat all ingredients together in a large bowl until just combined, about one minute, starting on low speed.

Increase speed to high and beat until stiff peaks form. This will take about three minutes in a stand mixer or up to 10 minutes with a handheld mixer.

Use line and flood method, detailed below, to ice cookies.

Spoon about ¼ of the icing into a disposable piping bag and snip off a tiny bit of the bag's tip. Draw a line of icing as close as you'd like to the outer edge of your cookie, making sure to connect the line's ends to each other so the flood icing won't have any gaps to flow out.

In a medium bowl, mix some more of the icing with two additional teaspoons of water. This icing should be thin enough to spread slowly and slightly across the surface of the cookies, but no thinner than that. You may need to experiment a little to find the consistency that's best for your humidity and, ahem, skill level. Pour this icing into another piping bag or better yet a squeeze bottle.

Squeeze some flood icing onto the surface of a cookie, filling in the entire surface inside the line. You can use a toothpick to fill any gaps that don't fill themselves and gently rap the cookie onto the work surface if you're brave and want a perfectly smooth finish.

Let dry completely.