Whisk dry ingredients: In a medium bowl, whisk together the flour, baking powder, and salt.
Cream butter and sugar: In a large bowl, using an electric mixer, cream together the softened butter and granulated sugar until light and fluffy.
Add egg and vanilla: Beat in the egg and egg yolk, then add the vanilla extract. Mix until just combined.
Gradually add dry ingredients: With the mixer on low speed, gradually add the dry ingredients to the wet ingredients. Mix until just combined.
Chill the dough: Divide the dough in half, flatten each half into a disk, and wrap each disk tightly in plastic wrap. Refrigerate for at least 2 hours.
Preheat and prepare: Preheat oven to 375°F (190°C). Line baking sheets with parchment paper.
Roll out the dough: Lightly flour a clean work surface and roll out the dough to about 1/4-inch thickness.
Cut out shapes: Use cookie cutters to cut out shapes and place them onto baking sheets.
Bake: Bake for 8-10 minutes, or until edges are very lightly golden brown.
Cool: Let the cookies cool on baking sheets before transferring to a wire rack to cool completely.