For Sugar Cookies: Cream butter and 1 2/3 cups sugar in bowl of an electric mixer and beat until fluffy, about 5 minutes.
Add vanilla, baking powder and salt and beat at medium speed until mixed.
Add eggs; beat until blended.
Add flour and mix at low speed until combined, scraping down bowl once or twice. For Spice Cookies: Beat 2 Tbsp. sugar, ginger, cinnamon and allspice into full batch of Sugar Cookie dough. For Lemon Cookies: Beat lemon zest into full batch of Sugar Cookie dough. For Chocolate Cookies: Follow Step 1, but add cocoa powder after beating in eggs and then add only 2 2/3 cups flour.
Divide dough in half. Using hands, shape dough into discs, wrap tightly in plastic wrap and chill until firm, at least 1 hour and up to 2 days.
Arrange racks in upper and lower thirds of oven and preheat oven to 350F. Line 2 large cookie sheets with parchment.
Remove 1 disc of dough from refrigerator.
Roll out on a lightly floured surface to 1/4-inch to 1/8-inch thickness.
Cut cookies into stars, snowflakes or any other shapes.
Transfer cookies, with a metal spatula, to baking sheets and chill for 10 minutes.
Bake cookies 12 to 15 minutes, depending upon thickness and size, rotating pans halfway through, until golden and firm to touch. Cool for 5 minutes, transfer with a metal spatula to racks and let cool. Repeat with remaining dough.
To decorate cookies with solid icing, put some Royal Icing in a pastry bag with a small plain, round tip. (Or put icing in a sturdy plastic bag and snip a tiny hole in one corner.) Pipe around edge of each cookie and let dry. Stir 1 Tbsp. water into another portion of Royal Icing to soften; put thinned icing in a clean pastry bag or new plastic bag. Pipe icing onto each cookie, flooding inside of border.
Let dry. Re-pipe border.
Sprinkle cookie with sanding sugar, shake off excess and let dry.
To decorate cookies with stripes and dots, use thicker icing and pipe designs as shown in photos. (Cookies may be stored, tightly covered, in a tin for up to 2 weeks.)
