Makes about 4 dozen 3-inch cookies
For the cookies:
3 ½ cups all-purpose flour
1 tsp salt
2 sticks unsalted butter, room temperature
¾ cup granulated sugar
1 Tbl finely grated lemon zest (from about 1 lemon)\
1 Tbl very finely chopped fresh rosemary
1 large egg
1 tsp pure vanilla
For the icing:
1 large egg white
1 ½ cups plus 2 Tbl powdered sugar, more if needed
½ tsp fresh lemon juice
With an electric hand mixer or an electric stand mixer fitted with the paddle attachment, beat the butter and sugar on medium speed until light and fluffy, about 3 minutes. Add the lemon zest and rosemary and mix to combine well. Add the egg and vanilla, then continue to beat until well blended and smooth, about 1 minute more. Reduce the speed to low, and gradually add the flour mixture. Mix only until the dough is just combined, being careful not to over-mix. Divide the dough into two equal portions. Roll out half of the dough between two pieces of parchment paper, to a thickness of 3/16-inch. Slide the dough and parchment to a cookie sheet and refrigerate until firm, about 30 minutes. Repeat with the remaining dough.
Pre-heat the oven to 350°F and arrange the racks in the upper and lower thirds of the oven. Line two cookie sheets with parchment paper.
Using a 3-inch tall Christmas tree cookie cutter, cut out the cookies and arrange 1-inch apart on the prepared cookie sheets. Press the dough scraps together, roll again, and cut again. (If the dough becomes too soft, refrigerate for a little while.) Repeat re-rolling and re-cutting one more time, and then discard the scraps. When you have available cookie sheets, repeat with the remaining dough.
Bake, 2 sheets at a time, until the cookie edges are golden brown, about 10-12 minutes. Be sure to rotate the pans (trading their positions and turning them each 180 degrees) about half-way thorough. Cool the cookies on the pan for about five minutes, then transfer them to a wire rack to cool completely with a metal spatula.
To make the icing & frost the cookies: In a medium-sized mixing bowl, whisk together the egg white, sugar and lemon juice. Whisk until smooth.
Transfer the icing to a pastry bag with a small round tip. Pipe the icing just inside the edges of the cookie, to simply out-line the rim. If the icing is too thick to pipe, squeeze it back into the bowl and whisk in water, one drop at a time, until it pipes easily but still retains its shape. If it is too thin, whisk in more powdered sugar, 1 teaspoon at a time.