Measure out and cream together the softened butter and granulated sugar in a large mixing bowl using a hand or stand mixer on medium speed until the mixture is light and fluffy, about 2-3 minutes. Observe the mixture turning pale and creamy, with increased volume.
1 cup unsalted butter, 1 cup granulated sugar
Add the egg and vanilla extract to the creamed mixture. Mix on low speed until fully incorporated, about 30 seconds, until the mixture is smooth and slightly glossy.
1 large egg, 2 teaspoons vanilla extract
In a separate bowl, whisk together the all-purpose flour and baking powder. Gradually add this dry mixture to the wet ingredients, mixing on low speed or stirring with a spatula until evenly combined. The dough should come together in a cohesive ball. Stop mixing once the flour is just incorporated to avoid overworking the dough.
2 ¾ cups all-purpose flour, ½ teaspoon baking powder
Lightly flour a clean work surface and rolling pin. Roll out the dough to about ¼ inch thickness, ensuring an even surface. Use cookie cutters to cut out shapes, pressing firmly and lifting carefully to maintain the shapes.
Transfer the cut cookies onto a parchment-lined baking sheet, spacing them about 1 inch apart. Place the sheet in a preheated oven at 350°F (175°C) and bake for 8-10 minutes, or until the edges are lightly golden. Listen for a slight bubbling sound and observe the edges turning a faint golden hue as signs of doneness.
Remove the baked cookies from the oven and allow them to cool on the baking sheet for 5 minutes. Then transfer them to a wire rack to cool completely, revealing a smooth, matte surface with slightly crisp edges.