In the bowl of a stand mixer or a large mixing bowl, cream together the butter and sugar on medium-high speed until smooth, 1-2 minutes. Add the egg, vanilla bean paste and lemon zest and beat until combined. Decrease speed to low and add the flour and salt, mixing until just combined. Form the dough into a disc, wrap tightly with plastic wrap and refrigerate until completely chilled and firm, 1-2 hours.

When ready to bake, remove dough from refrigerator. Heat oven to 375º. Line baking sheets with parchment paper or nonstick baking mats. On a well floured surface, roll the dough to ¼-inch thickness. Cut with cookie cutters and transfer to baking sheets. Bake for 8-10 minutes, rotating the sheets halfway through, until the cookies are fully cooked but not at all browned. These cookies will harden as they cool, so take that into account when testing for doneness.

Allow to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. Gather dough scraps, roll again, and repeat cutting and baking process. Refrigerate dough as needed during this process. Once all the cookies are baked and cooled, decorate as desired.

To make the royal icing, combine all ingredients in the bowl of a stand mixer fitted with the paddle attachment and mix on low speed. Mix until the ingredients are well combined and the sheen has disappeared, 7-10 minutes. Add water, about a tablespoon at a time, until the icing reaches a consistency appropriate for piping. If the icing is too thick, it will be difficult to pipe. Transfer to an airtight container, color as desired (gel colors work best) and transfer a small amount to a piping bag fitted with a #2 tip. Cover the icing that is not in use. Pipe around the edges of each cookie and allow this to harden for at least an hour.

Thin the remaining icing (if you’re not using it for piped designs on top of the flooded cookies) with additional water, a small amount at a time, until it reaches a consistency appropriate for flooding (the icing should drip off the spoon easily and disappear into the bowl within about 5 or so seconds). Transfer to a squeeze bottle and flood within the piped border of each cookie. Use a toothpick to move the icing to the edges, if needed. Allow to set, preferably overnight, until the icing is hard and matte.

If desired, use any remaining stiff icing to pipe designs onto the flooded cookies. Allow to dry for an hour, then stack and store cookies in an airtight container.