For the Cookies:
15 ounces (3-1/3 cups) unbleached all-purpose flour
1 teaspoon table salt
8 ounces (1 cup) unsalted butter, at room temperature
3/4 cup granulated sugar
1 tablespoon finely grated lemon zest
1 tablespoon finely chopped fresh rosemary
1 large egg
1 teaspoon pure vanilla extract
Note: The risk of salmonella infection from consuming raw eggs is very low, but you can eliminate it entirely by using pasteurized eggs.
For the Icing:
1 large egg white (see note at right)
6-1/2 ounces (1-1/2 cups plus 2 tablespoons) confectioners' sugar; more as needed
1/2 teaspoon fresh lemon juice
Decorating sugar or edible dragees (optional)
Make the cookies:
In a medium bowl, whisk the flour and salt. With a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium speed until light and fluffy, about 2 minutes. Mix in the lemon zest and rosemary. Add the egg and vanilla; continue beating until well blended and smooth, about 30 seconds more. Reduce the speed to low and gradually add the dry ingredients. Mix until the dough is just combined; don't overmix. Divide the dough into 2 equal portions.
Roll one half of the dough between two sheets of parchment to an even 3/16-inch thickness. Slide the dough and parchment onto a cookie sheet and refrigerate until firm, about 30 minutes. Repeat with the remaining dough.
Position racks in the upper and lower thirds of the oven and heat the oven to 350°F. Line four cookie sheets with parchment.
Using a 3-1/2-inch (or similar) Christmas tree cookie cutter, cut out the cookies and arrange them 1 inch apart on the cookie sheets. Press the scraps together, reroll, and cut (if the dough becomes too soft to handle, chill until firm). Repeat one more time and then discard the scraps. Repeat with the remaining dough.
Bake two sheets at a time until the cookies' edges are golden brown, 10 to 12 minutes, rotating and swapping the sheets' positions halfway through for even baking. Cool the cookies on racks.
Make the icing:
In a medium bowl, whisk the egg white, sugar, and lemon juice until smooth. If not using immediately, transfer the icing to a small bowl and press plastic wrap directly onto the surface of the icing to prevent it from drying out.
Decorate the cookies:
Spoon some of the icing into a small pastry bag with a small (3/16 inch) plain tip. (Or use a small plastic bag and cut a tiny bit off a bottom corner of the bag.) Pipe the icing onto the cookies to outline the rim. (If the icing is too thick to pipe, put it back in the bowl and stir in water, a drop at a time, until it pipes easily but still retains its shape. If the icing is too thin, add confectioners' sugar, 1 teaspoon at a time.)
If using decorating sugar or dragées, apply them while the icing is wet. Once the icing is completely dry and hard, store the cookies in airtight containers in the refrigerator for up to 5 days.