3-1/4 cups unbleached all-purpose flour
1-1/2 tsp baking powder
1/2 tsp salt
1-1/4 cups best quality unsalted butter, softened
1 cup sugar
1 large egg
1 Tbsp milk
2-1/2 tsp best quality pure vanilla extract
Preheat oven to 375°F. Line a couple of baking sheets with a Silpat or parchment paper. In a large bowl, stir together flour, baking powder and salt. In another large bowl or the bowl of a heavy-duty stand mixer, beat together the butter and sugar, until fluffy. Add egg, milk and vanilla, and continue to beat until well blended and smooth. Beat flour mixture into the butter mixture until smooth. Divide dough in half. Place one half on a sheet of parchment paper or wax paper; cover with another sheet and roll to 1/4 inch. Repeat with second half of dough. Refrigerate dough for at least 30 minutes, or up to a couple of days (or, if making far in advance, you can freeze at this point. Wrap sheets tightly in plastic wrap). Remove one sheet from the refrigerator; peel off the top wax paper, then replace paper and invert dough. Peel off and discard what is now the top sheet of paper, and cut out the cookies. (cookies will spread, so do not place too close together on the baking sheet). Reroll scraps, refrigerating if necessary to firm the dough.
Bake for 6-9 minutes, or until just lightly colored on top and slightly darker at the edges. Rotate sheets halfway through for even browning. Remove pans from oven and let cookies cool 2-3 minutes. Then remove cookies to a rack and let cool completely. (At this point, the cookies can be stored in an airtight container for up to two weeks, in layers separated by parchment or wax paper.) After the cookies are completely cooled, decorate with Royal Icing.