Whisk together flour, baking powder, and salt.
Beat butter and granulated sugar with a mixer on medium speed until pale and fluffy, about 3 minutes. Beat in eggs, 1 at a time. Reduce speed to low; add flour mixture, and beat until combined. Add vanilla. Wrap dough in plastic, and refrigerate for 1 hour.
Preheat oven to 325 degrees. Roll out dough to 1/8-inch thickness on a lightly floured surface. Cut out egg shapes with a 2 1/2-inch oval cutter (sugarcraft.com). Transfer cookies to parchment-lined baking sheets, spacing about 1 inch apart. Refrigerate until firm, about 30 minutes. Bake until edges are golden, 8 to 10 minutes. Upon removing from oven, cut into pieces with a sharp knife (if they're cool, it will be difficult to create clean edges). Let cool. Using a pastry bag fitted with a
1/8-inch tip and filled with royal icing, decorate as desired. Sprinkle with sanding sugar while icing is wet. If adding dots or stripes, let base layer dry first.
Iced cookies can be stored at room temperature for up to 3 days.