Step 1: In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.
Step 2: In a large bowl, using an electric mixer, cream together the softened butter and 1½ cups granulated sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla extract.
Step 3: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix. The dough will be thick and sticky.
Step 4: Cover the bowl with plastic wrap and chill the dough in the refrigerator for at least 2 hours, or up to 2 days. This step is crucial for easy handling and proper crinkling.
Step 5: Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
Step 6: Place the ½ cup powdered sugar in a shallow bowl and the ¼ cup granulated sugar (if using) in another shallow bowl.
Step 7: Scoop out dough by the tablespoonful and roll into balls. First, roll each dough ball in the granulated sugar (if using), then generously coat it in the powdered sugar. Ensure a thick layer of powdered sugar completely covers the dough ball.
Step 8: Place the coated cookie dough balls about 2 inches apart on the prepared baking sheets.
Step 9: Bake for 10-12 minutes, or until the edges are set and the centers are still slightly soft. The powdered sugar will have crinkled beautifully.
Step 10: Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.