Using a mixer or whisk, beat together the softened butter and granulated sugar in a large mixing bowl until the mixture appears light and fluffy, about 3 minutes, and has a pale yellow color.
1 cup unsalted butter, 1 cup granulated sugar
Add the egg and vanilla extract to the bowl, then continue mixing until fully incorporated and the mixture is smooth, about 1 minute.
1 large egg, 2 teaspoons vanilla extract
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, mixing on low speed until a soft dough forms and begins to pull away from the sides of the bowl.
2 ¾ cups all-purpose flour, 1/2 teaspoon baking powder, 1/4 teaspoon salt
Divide the dough into two halves, then transfer each onto a lightly floured surface. Use a rolling pin to evenly roll each piece to about ¼ inch thickness.
Use cookie cutters to cut out shapes from the rolled dough, then transfer the shapes to a parchment-lined baking sheet, spacing them about 1 inch apart.
Bake the cookies in a preheated oven at 350°F (175°C) for 8-10 minutes, or until the edges are lightly golden and the surface shows slight cracking patterns. Remove from the oven and allow to cool on a wire rack for at least 10 minutes before serving.
